Exponentials

Problem 1

Find $h(3)$ for the function $h(x)=9 \cdot\left(\frac{1}{2}\right)^{x}$ .

See Solution

Problem 2

Identify the decreasing exponential function with a $y$ -intercept of 20 from these options: (1) $y=20\left(\frac{4}{3}\right)^{x}$ (2) $y=20\left(\frac{1}{2}\right)^{x}$ (3) $y=-2 x+20$ (4) $y=\left(\frac{1}{3}\right)^{x}+20$

See Solution

Problem 3

Find $f(0)$ for the function $f(x)=10(2)^{x}$ and describe its point on the graph of $y=f(x)$ .

See Solution

Problem 4

1. For the function $f(x)=10(2)^{x}$ , find $f(0)$ and its graph point. Is it increasing or decreasing? Compare average rates with $g(x)=10x+7$ . Sketch the graph.

See Solution

Problem 5

If $S(t)=250(1.045)^{t}$ , which statement is true about the initial deposit and interest rate?

See Solution

Problem 6

If $S(t)=250(1.045)^{t}$ , which statement about the initial deposit and interest rate is true?

See Solution

Problem 7

Model the depth of water in a pool draining at $20\%$ per hour from an initial depth of 12 feet. Find $D(t)$ for $t=1, 2, 3$ hours.

See Solution

Problem 8

Find the annual interest rate for an investment of \$3500 that doubles in 5 years. Options: 40\%, 50\%, 30\%, 20\%.

See Solution

Problem 9

Identify the function that represents exponential decay from the options below: a) $f(x)=8(17)^{\frac{x}{4}}$ b) $f(x)=3.4(0.4)^{2 x}$ c) $f(x)=25(8.0)^{x}$ d) $f(x)=6(1.01)^{x}$

See Solution

Problem 10

Identify the function representing exponential growth: a) $f(x)=8(1.7)^{\frac{x}{4}}$ b) $f(x)=25(0.8)^{x}$ c) $f(x)=6(0.91)^{x}$ d) $f(x)=3.4(0.54)^{2x}$

See Solution

Problem 11

Find the time $t$ when the total revenue $TR = 5 e^{-0.15t}$ equals 2 million dollars.

See Solution

Problem 12

Find $t$ when the GNP reaches 96 billion, given $GNP = 80 e^{0.02t}$ .

See Solution

Problem 13

Find the domain and range of the function $f(x)=4(2^{-2x+7})-5$ .

See Solution

Problem 14

Identify the transformation of the function $f(x)=-3\left(5^{2 x-6}\right)+3$ : a) Right 3 units b) Down 6 units c) Stretch by 3 d) Reflection on $y$ -axis

See Solution

Problem 15

In 2000, Mexico's population was 100 million, growing at $1.53 \%$ per year. When will it reach 109 million? Round to nearest year. a. 2006 b. 2008 c. 2005 d. 2007 (Select One)

See Solution

Problem 16

Write a recursive rule for the function $y=18(8)^{x}$ . Choose one:
A $f(0)=8$ , $f(n)=18 \circ f(n-1)$ B $f(0)=18$ , $f(n)=18 \cdot f(n-1)$ C $f(0)=18$ , $f(n)=8 \cdot f(n-1)$ D $f(0)=8$ , $f(n)=8 \cdot f(n-1)$

See Solution

Problem 17

Find the exponential function with an initial value of 3: $f(x)=\frac{1}{3}(9)^{x}$ or $f(x)=(3)^{x}$ .

See Solution

Problem 18

Determine which statement is true for the function $f(x)=a\left(2^{x}\right)$ given the values of $a$ and $f(0)$ or $f(1)$ .

See Solution

Problem 19

Find the growth factor of the function $f(x)=\frac{1}{5}\left(15^{x}\right)$ . Options: $\frac{1}{5}$ , $\frac{1}{3}$ , 5, 15.

See Solution

Problem 20

Find the half-life of a radioactive element that decays to $\frac{1}{\sqrt{2}}$ in 15 days.

See Solution

Problem 21

Is the transformation from $y=3^{x}$ to $y=5 \cdot 3^{-(x-2)}+9$ unique? List transformations to prove or disprove the claim.

See Solution

Problem 22

Find the missing quantity in the formula $A=P e^{r t}$ with $P=680,000$ , $r=12\%$ , and $t=8$ .

See Solution

Problem 23

Find the growth rate of a bacteria population starting at 100 that doubles every 6 hours. How many will there be in 2 days?

See Solution

Problem 24

Find the population of a city in the Philippines after 20 years using the model $A=50 e^{0.07 t}$ .

See Solution

Problem 25

Find the population in 2037 using the model $A=50 e^{0.07 t}$ , where $t$ is years after 1997.

See Solution

Problem 26

Find the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

See Solution

Problem 27

An investor owns an ETF tracking the ASX 200 with a $2\%$ dividend yield. Buy at \ $50, sell at \$49. Borrow at$ 7\% $, invest at$ 5.5\%$. Find the half-year forward price range with no arbitrage.

See Solution

Problem 28

Berapakah jumlah simpanan Puan Zainab selepas 5 tahun jika RM500 dideposit dengan faedah $4 \%$ setahun, dikompaun suku tahunan?

See Solution

Problem 29

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ , its domain and range. Sketch $f$ and $f^{-1}$ . Also, find $(f \cdot g)(x)$ for $g(x)=\ln 3x$ .

See Solution

Problem 30

Find the half-year forward price range for an ETF with a 2% dividend yield, bought at \$50 and sold at \$49, with borrowing at 7% and investing at 5.5%.

See Solution

Problem 31

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2 x-3}-2$ , its domain and range. Sketch $f$ and $f^{-1}$ . Calculate $(f \cdot g)(x)$ for $g(x)=\ln 3 x$ .

See Solution

Problem 32

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ and its domain/range. Sketch $f$ and $f^{-1}$ . For $g(x)=\ln 3x$ , find $(f \cdot g)(x)$ .

See Solution

Problem 33

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ , its domain/range, sketch $f$ and $f^{-1}$ , and compute $(f \cdot g)(x)$ for $g(x)=\ln 3x$ .

See Solution

Problem 34

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2 x-3}-2$ and its domain/range. Sketch $f$ and $f^{-1}$ . For $g(x)=\ln 3 x$ , find $(f \cdot g)(x)$ .

See Solution

Problem 35

How long to double an investment at $8.5\%$ p.a. interest, compounded quarterly?

See Solution

Problem 36

Find $x$ such that $3^{x+1} - 3^{x} - 54 = 0$ .

See Solution

Problem 37

Find the solutions for the equation $(e^{x}-1)(e^{x}+2)=0$ .

See Solution

Problem 38

Index the initial \$52000 investment for an average inflation of 3% per year over the investment period.

See Solution

Problem 39

Penny invests \$4800 at 11\% annual interest, compounded monthly, for 13 years. Find the interest earned after 13 years.

See Solution

Problem 40

Penny invests \$2400 at 11% annual interest, compounded monthly, for 13 years. Find the total interest earned.

See Solution

Problem 41

If you invest \ $3,200 and after 2 years you have \$800, what is the interest rate$ i $given by$ A=P(1+i)^{t}$?

See Solution

Problem 42

Solve the equation $216(6^{2r-1})=1$ .

See Solution

Problem 43

Solve the equation $2^{2(x+1)} - 9(2^{x}) + 2 = 0$ using the substitution $y = 2^{x}$ .

See Solution

Problem 44

Solve $5^{m} - 4(3^{m}) = 0$ and provide the answer to four significant figures.

See Solution

Problem 45

Ms. Warden wants \$20,000 in 4 years. How much to invest now at 8.5% annual interest, compounded semi-annually?

See Solution

Problem 46

Sketch the graph of the function $y=3.2^{x+1}-1$ .

See Solution

Problem 47

Find the principal amount deposited at $10\%$ p.a. if it grows to \$31,460 after 2 years.

See Solution

Problem 48

Find the compound interest on \$70000 at 6\% p.a. compounded monthly after 8 months.

See Solution

Problem 49

Find the principal amount deposited at 10% p.a. if it grows to \$31460 in 2 years.

See Solution

Problem 50

Find the average rate of change of the function from $x=3$ to $x=5$ . Options: A. 98 B. 49 C. 37 D. 76

See Solution

Problem 51

Identify the incorrect characteristic of an exponential function: A. Domain: all reals, B. Passes through $(0,1)$ , C. Through origin, D. Range: $y>0$ .

See Solution

Problem 52

Identify the exponential parent function from the options: A. $f(x)=x$ , B. $f(x)=2^{x}$ , C. $f(x)=|x|$ , D. $f(x)=x^{2}$ .

See Solution

Problem 53

Bestimme die Funktionsgleichung $f(x)=c \cdot a^{x}$ für Punkte $P$ und $Q$ . Finde $x$ für $f(x)=256$ .
Situationen: Wachstumsfaktor und prozentuale Veränderung für:
1. 2,6 kg auf 3,3 kg
2. nach $\frac{3}{4}$ Tag: 1/8
3. von 2400 € auf 850 €
4. 2002: 4,2\%, 2015: 2,2\%
5. 150 um 6 Uhr, 1500 um 18:30
6. alle 10 Jahre Verdopplung
Finde $x$ für: a) $f(x)=2^{x}$ , $y=64$ b) $f(x)=0,5^{x}$ , $y=\frac{1}{1024}$ c) $f(x)=10^{x}$ , $y=0,1$ d) $f(x)=5^{x}$ , $y=\frac{1}{125}$ e) $f(x)=9^{x}$ , $y=3$ f) $f(x)=8^{x}$ , $y=1$ g) $f(x)=16^{x}$ , $y=0,25$ h) $f(x)=\left(\frac{1}{3}\right)^{x}$ , $y=27$

See Solution

Problem 54

What is the new equation for the function after stretching $f(x)=2^{x}$ vertically by a factor of 3? A. $g(x)=2 \cdot 3^{x}$ B. $g(x)=3 \cdot 2^{x}$ C. $g(x)=2^{3 x}$ D. $g(x)=\frac{1}{3} \cdot 2^{x}$

See Solution

Problem 55

How does the graph of $f(x)=2^{x}$ change to $g(x)=3 \cdot 2^{x}+5$ ? Select all that apply: A, B, C, D, E.

See Solution

Problem 56

Find the inequality for hours $t$ after 6 a.m. when cars passing the tollbooth exceed 4,300, starting with 1,380 and increasing by $46\%$ each hour.

See Solution

Problem 57

Find the inequality for when trees drop to 621,859, given 691,255 trees decreasing at $1.5\%$ yearly. Solve for $t$ .

See Solution

Problem 58

Find the equation to determine when a stock at \ $102.15 grows to \$233.10 at an$ 8.6\%$ quarterly increase.

See Solution

Problem 59

Solve $625=5^{(7x-3)}$ for $x$ . Options: A. $x=2$ , B. $x=1$ , C. $x=-2$ , D. $x=-1$ .

See Solution

Problem 60

A zoo has a newborn elephant weighing 200 pounds. Its weight increases by half the previous month's weight. Which equation helps find $t$ for 675 pounds, and what is $t$ ? Options: $200\left(\frac{3}{2}\right)^{t}=675$ ; Solutions: 2, 3, 4, or 6 months?

See Solution

Problem 61

Bestimme die Funktionsgleichung $f(x)=c \cdot a^{x}$ durch die Punkte P und Q. Für welches $x$ gilt $f(x)=256$ ? a) $P(0 \mid 4)$ , $Q(4 \mid 0,5)$ b) $P(0 \mid 0,25)$ , $Q(6 \mid 16)$ c) $P(0 \mid 512)$ , $Q(-3 \mid 8)$

See Solution

Problem 62

Bestimme für welches $x$ die Funktion $f(x)$ den Wert $y$ hat: a) $f(x)=2^{x}$ , $y=64$ ; b) $f(x)=0,5^{x}$ , $y=\frac{1}{1024}$ ; c) $f(x)=10^{x}$ , $y=0,1$ ; d) $f(x)=5^{x}$ , $y=\frac{1}{125}$ .

See Solution

Problem 63

Calculate Mario's savings after 10 years with \ $1000 at 4\% interest using$ A=p(1+r)^{t}$. Options: a. \$2156.01 b. \$1004 c. \$1000 d. \$1428.24

See Solution

Problem 64

Kenny's spending increases by $8\%$ annually. If he spends \$50,700 now, what will he spend in 11 years?

See Solution

Problem 65

Solve: $6^{x}=6^{3x-12}$ . Find $x$ from the options: $-1$ , $6$ , $-2$ , $3$ .

See Solution

Problem 66

Caden takes a \$15,000 loan at 3.5\% interest, compounded monthly for 5 years. What is the total amount paid?

See Solution

Problem 67

Caden takes a \$15,000 loan at 3.5\% interest, compounded monthly, to be paid in 5 years. What is the total amount paid?

See Solution

Problem 68

To have \$500,000 in 20 years at 9% interest, how much to deposit monthly and total interest earned?

See Solution

Problem 69

Deposit $\$ 5000$ at $7\%$ interest compounded monthly. What is the total in 10 years?

See Solution

Problem 70

Find the maximum value of $y = x^{1/x}$ for $x > 0$ .

See Solution

Problem 71

A city with a current population of 500,000 grows at $0.95\%$ annually. Which model represents this growth? a. $500000(1+0,0095)^{t}$ . b. $500000\left(1+0,95^{t}\right)$ . c. $500000\left(0,095^{t}\right)$ . d. $500000+1,0095^{t}$ .

See Solution

Problem 72

A city’s population is 820,000 and grows at $0.4\%$ annually. Which model is correct for $t$ years from now? a. $820000(0.04^{t})$ b. $820000(1+0.004)^{t}$ c. $820000(1+0.4^{t})$ d. $820000+1.004^{t}$

See Solution

Problem 73

What is the balance after 15 years for a \ $1500 deposit at a 7% quarterly interest rate using$ F=P\left(1+\frac{r}{n}\right)^{n t}$?

See Solution

Problem 74

Denise invests in a bond with $3\%$ p.a. compound interest. She gets $\$ 3582$ after 6 years. Find her initial investment.

See Solution

Problem 75

Find the range of $f(x)=2^{x}-10$ for integers $x$ from -1 to 3. Which values are in the range? Options: -12, -10, -9, -6, -2.

See Solution

Problem 76

A bacterium triples every hour. Start with 90. Find the count at hour 5 using $a(n)=90 \cdot 3^{n-1}$ . Options: A. 21,870 B. 810 C. 7290 D. 1350

See Solution

Problem 77

Solve for $x$ in the equation $3 m^{x+1} = 18$ .

See Solution

Problem 78

Ben wants to buy a house for \$168,000. If it appreciates 1% annually, what will it be worth in 6 years? Round to the nearest dollar.

See Solution

Problem 79

Model the sales of electronic devices, $S(t)$ , since 1997 and find the annual growth rate from 1997 to 2009 when sales were 438 million.

See Solution

Problem 80

Find an increasing exponential function with the same vertical intercept as $f(x)=0.3x+2$ when $x=0$ .

See Solution

Problem 81

A bacterial colony of 1000 doubles in 12 hours. Find growth rate $k$ and time to reach 200,000 bacteria.

See Solution

Problem 82

Karen tests a bath fizzer weighing 5 ounces. It halves every minute. Find the equation $y=a(b)^{x}$ and weight after 3 minutes.

See Solution

Problem 83

Find $f(2)$ and $f(5)$ for the function defined as $f(x)=2^{x}$ .

See Solution

Problem 84

Antonio's county has a population of 66,500, decreasing by $4\%$ yearly. Model it with $y=a(b)^{x}$ and find $y$ in 10 years.

See Solution

Problem 85

Dr. Powell gave Ruby 40 micrograms of medication. Model the remaining amount with $y=40(0.8)^{x}$ . How much is left after 4 hours?

See Solution

Problem 86

Model Clover Hills' population with $y=a(b)^{x}$ , given it grew from 3,650 to 3,869 in 1 year. Predict after 4 years.

See Solution

Problem 87

Write an exponential equation $y=a(b)^{x}$ to model Lime County's declining population, starting with 711,500.

See Solution

Problem 88

Encik Amin simpan RM28,000 dengan faedah 3\% setahun, dikompaun setiap 3 bulan. Berapa jumlah simpanan pada akhir tahun $2022$ ?

See Solution

Problem 89

Calcula $a+b$ en el modelo de Jenss: $y=78+a x-e^{b-x}$ , sabiendo que $y(0)=55$ y $y(4)=103$ . Redondea a dos decimales.

See Solution

Problem 90

Find $f(\ln 3)$ for the function $f(x)=2 e^{2 x}$ .

See Solution

Problem 91

Nia invests \ $3100 at 2% annual interest. Find her account balance in year 4 using$ A(n)=3100(1+0.02)^{n-1}$. Round to nearest dollar.

See Solution

Problem 92

Find the value of a \ $1000 investment after 3 years using the formula$ 1000(1.1)^{t}$.

See Solution

Problem 93

Find the function for gas price starting at 2.25, increasing at 4% per year: $f(x)=2.25(1+0.04)^{x}$

See Solution

Problem 94

What is the monthly growth rate in the expression $f(x)=12(1.035)^{x}$ for a drama club? A. $0.35\%$ B. $1.035\%$ C. $3.5\%$ D. $12\%$

See Solution

Problem 95

Identify the initial value in Joanna's savings equation: $5,000\left(1+\frac{0.04}{12}\right)^{12 t}$ .

See Solution

Problem 96

Naomi's parents invest \$20,000 at 7% interest. How long to reach \$50,000? A. 13.5 B. 13.9 C. 14.1 D. 15.3 years

See Solution

Problem 97

What will be the future value of a $\$ 10,000$ investment at $5\%$ interest, compounded semiannually, in 5 years?

See Solution

Problem 98

Select the correct interpretation of $10,785(1.0275)^{x}$ for an investment with annual compounding interest.

See Solution

Problem 99

Interpret the expression $10,785(1.0275)^{x}$ : What are the initial investment and growth rate? Choose A, B, C, D, or E.

See Solution

Problem 100

Calculate the future value of a \$5,000 investment compounded annually at 10% for 10 years. Options: A. \$5,523 B. \$12,969 C. \$13,535 D. \$13,677

See Solution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Exponentials

Problem 1

Find h(3)h(3)h(3) for the function h(x)=9⋅(12)xh(x)=9 \cdot\left(\frac{1}{2}\right)^{x}h(x)=9⋅(21​)x.

Problem 2

Problem 3

Find f(0)f(0)f(0) for the function f(x)=10(2)xf(x)=10(2)^{x}f(x)=10(2)x and describe its point on the graph of y=f(x)y=f(x)y=f(x).

Problem 4

1. For the function f(x)=10(2)xf(x)=10(2)^{x}f(x)=10(2)x, find f(0)f(0)f(0) and its graph point. Is it increasing or decreasing? Compare average rates with g(x)=10x+7g(x)=10x+7g(x)=10x+7. Sketch the graph.

Problem 5

If S(t)=250(1.045)tS(t)=250(1.045)^{t}S(t)=250(1.045)t, which statement is true about the initial deposit and interest rate?

Problem 6

If S(t)=250(1.045)tS(t)=250(1.045)^{t}S(t)=250(1.045)t, which statement about the initial deposit and interest rate is true?

Problem 7

Model the depth of water in a pool draining at 20%20\%20% per hour from an initial depth of 12 feet. Find D(t)D(t)D(t) for t=1,2,3t=1, 2, 3t=1,2,3 hours.

Problem 8

Find the annual interest rate for an investment of \$3500 that doubles in 5 years. Options: 40\%, 50\%, 30\%, 20\%.

Problem 9

Identify the function that represents exponential decay from the options below: a) f(x)=8(17)x4f(x)=8(17)^{\frac{x}{4}}f(x)=8(17)4x​ b) f(x)=3.4(0.4)2xf(x)=3.4(0.4)^{2 x}f(x)=3.4(0.4)2x c) f(x)=25(8.0)xf(x)=25(8.0)^{x}f(x)=25(8.0)x d) f(x)=6(1.01)xf(x)=6(1.01)^{x}f(x)=6(1.01)x

Problem 10

Identify the function representing exponential growth: a) f(x)=8(1.7)x4f(x)=8(1.7)^{\frac{x}{4}}f(x)=8(1.7)4x​ b) f(x)=25(0.8)xf(x)=25(0.8)^{x}f(x)=25(0.8)x c) f(x)=6(0.91)xf(x)=6(0.91)^{x}f(x)=6(0.91)x d) f(x)=3.4(0.54)2xf(x)=3.4(0.54)^{2x}f(x)=3.4(0.54)2x

Problem 11

Find the time ttt when the total revenue TR=5e−0.15tTR = 5 e^{-0.15t}TR=5e−0.15t equals 2 million dollars.

Problem 12

Find ttt when the GNP reaches 96 billion, given GNP=80e0.02tGNP = 80 e^{0.02t}GNP=80e0.02t.

Problem 13

Find the domain and range of the function f(x)=4(2−2x+7)−5f(x)=4(2^{-2x+7})-5f(x)=4(2−2x+7)−5.

Problem 14

Identify the transformation of the function f(x)=−3(52x−6)+3f(x)=-3\left(5^{2 x-6}\right)+3f(x)=−3(52x−6)+3: a) Right 3 units b) Down 6 units c) Stretch by 3 d) Reflection on yyy-axis

Problem 15

In 2000, Mexico's population was 100 million, growing at 1.53%1.53 \%1.53% per year. When will it reach 109 million? Round to nearest year. a. 2006 b. 2008 c. 2005 d. 2007 (Select One)

Problem 16

Problem 17

Find the exponential function with an initial value of 3: f(x)=13(9)xf(x)=\frac{1}{3}(9)^{x}f(x)=31​(9)x or f(x)=(3)xf(x)=(3)^{x}f(x)=(3)x.

Problem 18

Determine which statement is true for the function f(x)=a(2x)f(x)=a\left(2^{x}\right)f(x)=a(2x) given the values of aaa and f(0)f(0)f(0) or f(1)f(1)f(1).

Problem 19

Find the growth factor of the function f(x)=15(15x)f(x)=\frac{1}{5}\left(15^{x}\right)f(x)=51​(15x). Options: 15\frac{1}{5}51​, 13\frac{1}{3}31​, 5, 15.

Problem 20

Find the half-life of a radioactive element that decays to 12\frac{1}{\sqrt{2}}2​1​ in 15 days.

Problem 21

Is the transformation from y=3xy=3^{x}y=3x to y=5⋅3−(x−2)+9y=5 \cdot 3^{-(x-2)}+9y=5⋅3−(x−2)+9 unique? List transformations to prove or disprove the claim.

Problem 22

Find the missing quantity in the formula A=PertA=P e^{r t}A=Pert with P=680,000P=680,000P=680,000, r=12%r=12\%r=12%, and t=8t=8t=8.

Problem 23

Find the growth rate of a bacteria population starting at 100 that doubles every 6 hours. How many will there be in 2 days?

Problem 24

Find the population of a city in the Philippines after 20 years using the model A=50e0.07tA=50 e^{0.07 t}A=50e0.07t.

Problem 25

Find the population in 2037 using the model A=50e0.07tA=50 e^{0.07 t}A=50e0.07t, where ttt is years after 1997.

Problem 26

Find the zero of the function f(x)=2(2)x−16f(x)=2(2)^{x}-16f(x)=2(2)x−16. Enter a number.

Problem 27

An investor owns an ETF tracking the ASX 200 with a 2%2\%2% dividend yield. Buy at \50,sellat$49.Borrowat50, sell at \$49. Borrow at 50,sellat$49.Borrowat7\%,investat, invest at ,investat5.5\%$. Find the half-year forward price range with no arbitrage.

Problem 28

Berapakah jumlah simpanan Puan Zainab selepas 5 tahun jika RM500 dideposit dengan faedah 4%4 \%4% setahun, dikompaun suku tahunan?

Problem 29

Find the inverse f−1(x)f^{-1}(x)f−1(x) of f(x)=e2x−3−2f(x)=e^{2x-3}-2f(x)=e2x−3−2, its domain and range. Sketch fff and f−1f^{-1}f−1. Also, find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) for g(x)=ln⁡3xg(x)=\ln 3xg(x)=ln3x.

Problem 30

Find the half-year forward price range for an ETF with a 2% dividend yield, bought at \$50 and sold at \$49, with borrowing at 7% and investing at 5.5%.

Problem 31

Find the inverse f−1(x)f^{-1}(x)f−1(x) of f(x)=e2x−3−2f(x)=e^{2 x-3}-2f(x)=e2x−3−2, its domain and range. Sketch fff and f−1f^{-1}f−1. Calculate (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) for g(x)=ln⁡3xg(x)=\ln 3 xg(x)=ln3x.

Problem 32

Find the inverse f−1(x)f^{-1}(x)f−1(x) of f(x)=e2x−3−2f(x)=e^{2x-3}-2f(x)=e2x−3−2 and its domain/range. Sketch fff and f−1f^{-1}f−1. For g(x)=ln⁡3xg(x)=\ln 3xg(x)=ln3x, find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x).

Problem 33

Find the inverse f−1(x)f^{-1}(x)f−1(x) of f(x)=e2x−3−2f(x)=e^{2x-3}-2f(x)=e2x−3−2, its domain/range, sketch fff and f−1f^{-1}f−1, and compute (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) for g(x)=ln⁡3xg(x)=\ln 3xg(x)=ln3x.

Problem 34

Find the inverse f−1(x)f^{-1}(x)f−1(x) of f(x)=e2x−3−2f(x)=e^{2 x-3}-2f(x)=e2x−3−2 and its domain/range. Sketch fff and f−1f^{-1}f−1. For g(x)=ln⁡3xg(x)=\ln 3 xg(x)=ln3x, find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x).

Problem 35

How long to double an investment at 8.5%8.5\%8.5% p.a. interest, compounded quarterly?

Problem 36

Find xxx such that 3x+1−3x−54=03^{x+1} - 3^{x} - 54 = 03x+1−3x−54=0.

Problem 37

Find the solutions for the equation (ex−1)(ex+2)=0(e^{x}-1)(e^{x}+2)=0(ex−1)(ex+2)=0.

Problem 38

Index the initial \$52000 investment for an average inflation of 3% per year over the investment period.

Problem 39

Penny invests \$4800 at 11\% annual interest, compounded monthly, for 13 years. Find the interest earned after 13 years.

Problem 40

Penny invests \$2400 at 11% annual interest, compounded monthly, for 13 years. Find the total interest earned.

Problem 41

Find $h(3)$ for the function $h(x)=9 \cdot\left(\frac{1}{2}\right)^{x}$ .

Find $f(0)$ for the function $f(x)=10(2)^{x}$ and describe its point on the graph of $y=f(x)$ .

1. For the function $f(x)=10(2)^{x}$ , find $f(0)$ and its graph point. Is it increasing or decreasing? Compare average rates with $g(x)=10x+7$ . Sketch the graph.

If $S(t)=250(1.045)^{t}$ , which statement is true about the initial deposit and interest rate?

If $S(t)=250(1.045)^{t}$ , which statement about the initial deposit and interest rate is true?

Model the depth of water in a pool draining at $20\%$ per hour from an initial depth of 12 feet. Find $D(t)$ for $t=1, 2, 3$ hours.

Identify the function that represents exponential decay from the options below: a) $f(x)=8(17)^{\frac{x}{4}}$ b) $f(x)=3.4(0.4)^{2 x}$ c) $f(x)=25(8.0)^{x}$ d) $f(x)=6(1.01)^{x}$

Identify the function representing exponential growth: a) $f(x)=8(1.7)^{\frac{x}{4}}$ b) $f(x)=25(0.8)^{x}$ c) $f(x)=6(0.91)^{x}$ d) $f(x)=3.4(0.54)^{2x}$

Find the time $t$ when the total revenue $TR = 5 e^{-0.15t}$ equals 2 million dollars.

Find $t$ when the GNP reaches 96 billion, given $GNP = 80 e^{0.02t}$ .

Find the domain and range of the function $f(x)=4(2^{-2x+7})-5$ .

Identify the transformation of the function $f(x)=-3\left(5^{2 x-6}\right)+3$ : a) Right 3 units b) Down 6 units c) Stretch by 3 d) Reflection on $y$ -axis

In 2000, Mexico's population was 100 million, growing at $1.53 \%$ per year. When will it reach 109 million? Round to nearest year. a. 2006 b. 2008 c. 2005 d. 2007 (Select One)

Find the exponential function with an initial value of 3: $f(x)=\frac{1}{3}(9)^{x}$ or $f(x)=(3)^{x}$ .

Determine which statement is true for the function $f(x)=a\left(2^{x}\right)$ given the values of $a$ and $f(0)$ or $f(1)$ .

Find the growth factor of the function $f(x)=\frac{1}{5}\left(15^{x}\right)$ . Options: $\frac{1}{5}$ , $\frac{1}{3}$ , 5, 15.

Find the half-life of a radioactive element that decays to $\frac{1}{\sqrt{2}}$ in 15 days.

Is the transformation from $y=3^{x}$ to $y=5 \cdot 3^{-(x-2)}+9$ unique? List transformations to prove or disprove the claim.

Find the missing quantity in the formula $A=P e^{r t}$ with $P=680,000$ , $r=12\%$ , and $t=8$ .

Find the population of a city in the Philippines after 20 years using the model $A=50 e^{0.07 t}$ .

Find the population in 2037 using the model $A=50 e^{0.07 t}$ , where $t$ is years after 1997.

Find the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

An investor owns an ETF tracking the ASX 200 with a $2\%$ dividend yield. Buy at \ $50, sell at \$49. Borrow at$ 7\% $, invest at$ 5.5\%$. Find the half-year forward price range with no arbitrage.

Berapakah jumlah simpanan Puan Zainab selepas 5 tahun jika RM500 dideposit dengan faedah $4 \%$ setahun, dikompaun suku tahunan?

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ , its domain and range. Sketch $f$ and $f^{-1}$ . Also, find $(f \cdot g)(x)$ for $g(x)=\ln 3x$ .

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2 x-3}-2$ , its domain and range. Sketch $f$ and $f^{-1}$ . Calculate $(f \cdot g)(x)$ for $g(x)=\ln 3 x$ .

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ and its domain/range. Sketch $f$ and $f^{-1}$ . For $g(x)=\ln 3x$ , find $(f \cdot g)(x)$ .

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ , its domain/range, sketch $f$ and $f^{-1}$ , and compute $(f \cdot g)(x)$ for $g(x)=\ln 3x$ .

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2 x-3}-2$ and its domain/range. Sketch $f$ and $f^{-1}$ . For $g(x)=\ln 3 x$ , find $(f \cdot g)(x)$ .

How long to double an investment at $8.5\%$ p.a. interest, compounded quarterly?

Find $x$ such that $3^{x+1} - 3^{x} - 54 = 0$ .

Find the solutions for the equation $(e^{x}-1)(e^{x}+2)=0$ .

If you invest \ $3,200 and after 2 years you have \$800, what is the interest rate$ i $given by$ A=P(1+i)^{t}$?

Solve the equation $216(6^{2r-1})=1$ .

Solve the equation $2^{2(x+1)} - 9(2^{x}) + 2 = 0$ using the substitution $y = 2^{x}$ .

Solve $5^{m} - 4(3^{m}) = 0$ and provide the answer to four significant figures.

Sketch the graph of the function $y=3.2^{x+1}-1$ .

Find the principal amount deposited at $10\%$ p.a. if it grows to \$31,460 after 2 years.

Find the average rate of change of the function from $x=3$ to $x=5$ . Options: A. 98 B. 49 C. 37 D. 76

Identify the incorrect characteristic of an exponential function: A. Domain: all reals, B. Passes through $(0,1)$ , C. Through origin, D. Range: $y>0$ .

Identify the exponential parent function from the options: A. $f(x)=x$ , B. $f(x)=2^{x}$ , C. $f(x)=|x|$ , D. $f(x)=x^{2}$ .

What is the new equation for the function after stretching $f(x)=2^{x}$ vertically by a factor of 3? A. $g(x)=2 \cdot 3^{x}$ B. $g(x)=3 \cdot 2^{x}$ C. $g(x)=2^{3 x}$ D. $g(x)=\frac{1}{3} \cdot 2^{x}$

How does the graph of $f(x)=2^{x}$ change to $g(x)=3 \cdot 2^{x}+5$ ? Select all that apply: A, B, C, D, E.

Find the inequality for hours $t$ after 6 a.m. when cars passing the tollbooth exceed 4,300, starting with 1,380 and increasing by $46\%$ each hour.

Find the inequality for when trees drop to 621,859, given 691,255 trees decreasing at $1.5\%$ yearly. Solve for $t$ .

Find the equation to determine when a stock at \ $102.15 grows to \$233.10 at an$ 8.6\%$ quarterly increase.

Solve $625=5^{(7x-3)}$ for $x$ . Options: A. $x=2$ , B. $x=1$ , C. $x=-2$ , D. $x=-1$ .

A zoo has a newborn elephant weighing 200 pounds. Its weight increases by half the previous month's weight. Which equation helps find $t$ for 675 pounds, and what is $t$ ? Options: $200\left(\frac{3}{2}\right)^{t}=675$ ; Solutions: 2, 3, 4, or 6 months?

Bestimme für welches $x$ die Funktion $f(x)$ den Wert $y$ hat: a) $f(x)=2^{x}$ , $y=64$ ; b) $f(x)=0,5^{x}$ , $y=\frac{1}{1024}$ ; c) $f(x)=10^{x}$ , $y=0,1$ ; d) $f(x)=5^{x}$ , $y=\frac{1}{125}$ .

Calculate Mario's savings after 10 years with \ $1000 at 4\% interest using$ A=p(1+r)^{t}$. Options: a. \$2156.01 b. \$1004 c. \$1000 d. \$1428.24

Kenny's spending increases by $8\%$ annually. If he spends \$50,700 now, what will he spend in 11 years?

Solve: $6^{x}=6^{3x-12}$ . Find $x$ from the options: $-1$ , $6$ , $-2$ , $3$ .

Deposit $\$ 5000$ at $7\%$ interest compounded monthly. What is the total in 10 years?

Find the maximum value of $y = x^{1/x}$ for $x > 0$ .

What is the balance after 15 years for a \ $1500 deposit at a 7% quarterly interest rate using$ F=P\left(1+\frac{r}{n}\right)^{n t}$?

Denise invests in a bond with $3\%$ p.a. compound interest. She gets $\$ 3582$ after 6 years. Find her initial investment.