Deck 4: Exponential Functions, Logarithms, and E

Question 1

How much would an initial amount of $4,000, compounded continuously at 5% annual interest, become after 10 years?

Answer 1

$6,594.89

Question 2

How much would an initial amount of $5,000, compounded continuously at 8% annual interest, become after 28 years?

Answer 2

$46,966.66

Question 3

How much would you need to deposit in a bank account paying 4% annual interest compounded continuously so that at the end of 2 years you would have $10,000?

A) $9,231.16
B) $9,607.89
C) $10,832.87
D) $10,408.11

Answer 3

$9,231.16

Question 4

How much would you need to deposit in a bank account paying 4% annual interest compounded continuously so that at the end of 19 years you would have $20,000?

Question 5

Suppose that a bank account that compounds interest continuously grows from $1000 to $1100 in 5 years. What annual interest rate is the bank paying? Round your answer to one decimal place.

Question 6

Suppose that a bank account that compounds interest continuously grows from $200 to $310 in three years. What annual interest rate is the bank paying? Round your answer to one decimal place.

Question 7

Suppose a colony of bacteria has a continuous growth rate of 18% per hour. By what percent will the colony have grown after 5 hours?

A) 40.7%
B) 246.0%
C) 60.7%
D) 146.0%

Question 8

Suppose a colony of bacteria has a continuous growth rate of 20% per hour. By what percent will the colony have grown after 2 hours? Round your answer to the nearest tenth.

Question 9

Suppose a country's population increases by a total of 5% over a 2-year period. What is the continuous growth rate for this country? Round your answer to the nearest hundredth.

Question 10

Suppose a country's population increases by a total of 17% over a 7-year period. What is the continuous growth rate for this country? Round your answer to the nearest hundredth.

Question 11

Suppose that the amount of the world's computer hard disk storage increases by a total of 300% over a 9-year period. What is the continuous growth rate for the amount of the world's hard disk storage?

A) 7.7%
B) 0.9%
C) 15.4%
D) 1.7%

Question 12

Suppose that a colony of bacteria has a continuous growth rate of 28% per hour. If the colony contains 10,000 cells now, how many did it contain 8 hours ago?

Question 13

Suppose that a colony of bacteria has a continuous growth rate of 33% per hour. How many hours does it take the colony to triple in size? Round your answer to the nearest hundredth.

Question 14

About how many years does it take for money to double when compounded continuously at 4% per year?

A) 35
B) 9
C) 18
D) 17

Question 15

About how many years does it take for $200 to become $800 when compounded continuously at 5% per year?

Question 16

How many years does it take for money to triple when compounded continuously at 9% per year? Round your answer to the nearest year.

Question 17

Find a formula for estimating how long money takes to increase by a factor of 9 at R percent annual interest compounded continuously.

A)

B)

C)

D)

Question 18

Suppose one bank account pays 8% annual interest compounded once per year, and a second bank account pays 8% annual interest compounded continuously. If both bank accounts start with the same initial amount, how many years will it take for the second bank account to contain double the amount of the first bank account?

Question 19

Suppose one bank account pays 9% annual interest compounded once per year, and a second bank account pays 10% annual interest compounded continuously. If both bank accounts start with the same initial amount, how many years will it take for the second bank account to contain 50% more than the first bank account?

Question 20

Suppose a colony of bacteria has doubled in 9 hours. What is the approximate percent per hour continuous growth rate of this colony of bacteria? Round your answer to the nearest whole percent.

Question 21

Estimate the indicated value without using a calculator.

Question 22

Estimate the indicated value without using a calculator.

Question 23

Estimate the indicated value without using a calculator.

Question 24

Estimate the indicated value without using a calculator.

Question 25

Estimate the indicated value without using a calculator.

Question 26

Estimate the indicated value without using a calculator.

A) 0.9995
B) 1.0005
C) 0.995
D) 1.005

Question 27

Estimate the indicated value without using a calculator.

Question 28

Estimate the value of

Round your answer to the nearest thousandth.

Question 29

Estimate the value of

A) 6.69
B) 0.15
C) 1.21
D) 0.83

Question 30

Estimate the value of
. Give the answer as a power of e.

Question 31

Estimate the value of . Give the answer as a power of e.

Question 32

Estimate the value of
. Give the answer as a power of e.

Question 33

Estimate the value of . Give the answer as a power of e.

Question 34

Estimate the slope of the line containing the points (5, ln 5) and

A)

B)

C) 5
D) -5

Question 35

Estimate the slope of the line containing the points (5, ln 5) and

Question 36

Suppose that t is a small positive number. Estimate the slope of the line containing the points And

A)

B)

C)

D)

Question 37

Suppose that r is a small positive number. Estimate the slope of the line containing the points and Give the answer as a power of e.

Question 38

Find a number r such that Give the answer as a natural log.

Question 39

Find a number t such that Round your answer to five decimal places.

Question 40

Find a number c such that

A) 44.3
B) 5,961.9
C) 17,885.7
D) 806.9

Question 41

For x = 6 and y = 7, evaluate each of the following. Round your answers to four decimal places.

A) ln(x + y)
B) ln x + ln y

Question 42

For x = 12 and y = 13, evaluate each of the following. Round your answers to four decimal places.

A) B)

Question 43

For x = 8 and y = 9, evaluate each of the following. Round your answers to four decimal places.

A)
B)

Question 44

Find a number y such that ln y = 3.

A)

B)

C)

D)

Question 45

Find a number c such that ln c = -8.

Question 46

Find a number t such that ln(3t - 4) = 3.

Question 47

Find all numbers x such that ln(x² - 3) = 4.

Question 48

Find a number x such that .

A)

B)

C)

D)

Question 49

Find all numbers x that satisfy the given equation.
ln(x + 6) - ln(x - 6) = 5

Question 50

Find all numbers x that satisfy the given equation.
Ln(x + 6) + ln(x - 6) = 4

A)

B)

C)

D)

Question 51

Find all numbers x that satisfy the given equation.

Question 52

Find the number c such that

Question 53

Find the number t that makes
As small as possible.

A) -8
B) 16
C) -16
D) 8

Question 54

Find a number x such that

Question 55

Find a number y such that

Question 56

Find a formula for Assuming that f(x) = ln x and

A) 8x
B) -8x
C)

D)

Question 57

Find a formula for assuming that
and g(x) = ln x .

Question 58

Assuming that f is a function defined by f(x) = 6 - 9ln(x).

A) Find the domain of f.
B) Find the range of f.
C) Find a formula for f ^-1.

Question 59

Assuming that f is a function defined by f(x) = 3 + ln(x + 8).

A) Find the domain of f.
B) Find the range of f.
C) Find a formula for f ^-1.

Question 60

Assuming that f is a function defined by .

A) Find the domain of f.
B) Find the range of f.
C) Find a formula for f ^-1.

Question 61

Find all numbers x such that e^2x + e^x = 20. Round the answer to 4 decimal places.

Question 62

What is the area of the region under the curve
, above the x-axis, and between the lines x = 1 and x = e¹¹.

Question 63

Given that 2¹⁰ $\approx$ 10³, find the value of A such that
.

Question 64

Given that 2¹⁰ $\approx$ 10³, determine which of the two numbers is larger.

Question 65

Without using a calculator or computer, give a rough estimate of .

A)

B)

C)

D)

Question 66

Without using a calculator or computer, determine which of the two numbers is larger.

A) is larger than
B) is larger than
C) They are equal to each other
D) Cannot be determined

Question 67

Suppose that you deposit into a savings account one dime on January 1, two dimes on January 2, four dines on January 3, and so on, doubling the amount of your deposit each day. After how many days, will your daily deposit exceed $100,000,000?

Question 68

Suppose that you deposit into a savings account one cent on January 1, five cents on January 2, twenty five cents on January 3, and so on, quintupling the amount of your deposit each day. What is the first day that your daily deposit will exceed $10,000?

A) January 6
B) January 7
C) January 8
D) January 9

Question 69

Suppose that a colony of bacteria starts with 50 cells and quadruples in size every 3 hours. Approximately how many cells will be in the colony after 2 hours?

A) 126
B) 800
C) 123
D) 3,200

Question 70

Suppose $900 is deposited in a bank account paying 1% interest per year, compounded 12 times per year. How much will be in the bank account at the end of 12 years? Round your answer to the nearest cent.

Question 71

Suppose $3,200 is deposited in a bank CD account paying 6% interest per year, compounded 2 times per year. How much will be in the CD account at the end of 16 years? Round your answer to the nearest cent.

A) $20,650.84
B) $8,240.26
C) $8,129.13
D) $5,135.06

Question 72

Suppose that a bank account paying 6% interest per year, compounded 4 times per year, contains $7,733 at the end of 14 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Question 73

Suppose that a bank account paying 3% interest per year, compounded 3 times per year, contains $44,900 at the end of 15 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

A) $28,820.43
B) $28,944.55
C) $28,693.57
D) $28,819.60

Question 74

Suppose a savings account pays 5% interest per year, compounded twice per year. If the savings accounts starts with $700, how many years would it take for the savings account to exceed $4,000?

Question 75

Suppose a savings account pays 8% interest per year, compounded 6 times per year. If the savings accounts starts with $1,300, how long would it take for the savings account to exceed $6,800?

A) 20 years
B) 19 years
C) 22 years
D) 21 years

Question 76

Suppose a bank wants to advertise that $2,000 deposited in its savings account will grow to $2060 in one year. This bank compounds interest 4 times per year. What annual interest rate must the bank pay? Round your answer to one decimal place.

Question 77

Suppose a bank wants to advertise that $2,000 deposited in its savings account will double in four years. This bank compounds interest 360 times per year. What annual interest rate must the bank pay?

A) 18.33%
B) 17.33%
C) 69.38%
D) 16.33%

Question 78

A certain rodent colony of 80 individuals doubles its size every 11 months. How many months would it takes to this colony to reach the critical population of 10,000 individuals?

Question 79

is $2^{13,746} < 13,746^{1000}$ correct?

Question 80

Every function f with exponential growth can be represented by a formula of the form $f(x) = cb^x$ for appropriate choices of c and b.