Question 1

Find the smallest integer M such that  
 .

Accepted Answer

A)  69,315 
B)  69,316 
C)  0 
D)  2

Question 2

Evaluate assuming that log₃x = 12.3 and log₃y = 7.9.

Accepted Answer

The answer of Evaluate assuming that log₃x =...

Question 3

Find a number x such that 102x + 10x = 30. Round your answer to four decimal places.

Accepted Answer

A)  -0.7782 
B)  -0.6990 
C)  0.7782 
D)  0.6990

Question 4

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

Accepted Answer

The answer of Find all numbers x that satisfy the...

Question 5

Estimate the indicated value without using a calculator.

Accepted Answer

The answer of Estimate the indicated value without using a...

Question 6

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.

Accepted Answer

The answer of Suppose a colony of bacteria has a...

Question 7

The full moon has an apparent magnitude of approximately -12.6. What would be the apparent magnitude of a star that was 14 times brighter than the full moon?

Accepted Answer

A)  -15.47 
B)  9.73 
C)  2.87 
D)  0.46

Question 8

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?

Accepted Answer

The answer of Suppose that you deposit into a savings...

Question 9

Evaluate the indicated expression. log ₃ 27

Accepted Answer

The answer of Evaluate the indicated expression. log ₃ 27...

Question 10

Evaluate Assuming that   .

Accepted Answer

A)  -16.1 
B)  16.1 
C)  -17.9 
D)  17.9

Question 11

Find an integer k such that 19^k has 308 digits.

Accepted Answer

The answer of Find an integer k such that 19^k...

Question 12

Estimate the indicated value without using a calculator.

Accepted Answer

The answer of Estimate the indicated value without using a...

Question 13

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?

Accepted Answer

The answer of Suppose that a colony of bacteria has...

Question 14

Every function f with exponential growth can be represented by a formula of the form $f(x) = c2^{kx}$ for appropriate choices of c and k.

Accepted Answer

A) True 
 B)False

Question 15

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

Accepted Answer

The answer of Estimate the value of   ...

Question 16

Find a formula for (f  g)(x) assuming that  
 .

Accepted Answer

The answer of Find a formula for (f  g)(x)...

Question 17

Suppose x is such that   . Evaluate   . Round your answer to three decimal places.

Accepted Answer

A)  245.25 
B)  187.250 
C)  7.457 
D)  6,271.25

Question 18

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

Accepted Answer

The answer of Estimate the value of 
  ...

Question 19

Evaluate   assuming that  
 .

Accepted Answer

The answer of Evaluate   assuming that  
...

Question 20

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

Accepted Answer

A) True 
 B)False

Exam 4: Exponential Functions, Logarithms, and E

Find the smallest integer M such that .

Evaluate assuming that log₃x = 12.3 and log₃y = 7.9.

Find a number x such that 10²^x + 10^x = 30. Round your answer to four decimal places.

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

Estimate the indicated value without using a calculator.

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.

The full moon has an apparent magnitude of approximately -12.6. What would be the apparent magnitude of a star that was 14 times brighter than the full moon?

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?

Evaluate the indicated expression. log ₃ 27

Evaluate Assuming that .

Find an integer k such that 19^k has 308 digits.

Estimate the indicated value without using a calculator.

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?

Every function f with exponential growth can be represented by a formula of the form $f(x) = c2^{kx}$ for appropriate choices of c and k.

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

Find a formula for (f g)(x) assuming that .

Suppose x is such that . Evaluate . Round your answer to three decimal places.

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

Evaluate assuming that .

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

Exam 4: Exponential Functions, Logarithms, and E

Find the smallest integer M such that .

Evaluate assuming that log3x = 12.3 and log3y = 7.9.

Find a number x such that 102x + 10x = 30. Round your answer to four decimal places.

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

Estimate the indicated value without using a calculator.

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.

The full moon has an apparent magnitude of approximately -12.6. What would be the apparent magnitude of a star that was 14 times brighter than the full moon?

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?

Evaluate the indicated expression. log 3 27

Evaluate Assuming that .

Find an integer k such that 19k has 308 digits.

Estimate the indicated value without using a calculator.

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?

Every function f with exponential growth can be represented by a formula of the form f(x)=c2kxf(x) = c2^{kx}f(x)=c2kx for appropriate choices of c and k.

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

Find a formula for (f g)(x) assuming that .

Suppose x is such that . Evaluate . Round your answer to three decimal places.

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

Evaluate assuming that .

is 213,746<13,74610002^{13,746} < 13,746^{1000}213,746<13,7461000 correct?

Evaluate assuming that log₃x = 12.3 and log₃y = 7.9.

Find a number x such that 10²^x + 10^x = 30. Round your answer to four decimal places.

Evaluate the indicated expression. log ₃ 27

Find an integer k such that 19^k has 308 digits.

Every function f with exponential growth can be represented by a formula of the form $f(x) = c2^{kx}$ for appropriate choices of c and k.

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