Question 1

The population P of a city grows exponentially according to the function   where t is measured in years. Find the population at time   .

Accepted Answer

A) 32,364 people 
B) 21,280 people 
C) 10,580 people 
D) 16,091 people 
E) 9200 people 
A) 32,364 people 
B) 21,280 people 
C) 10,580 people 
D) 16,091 people 
E) 9200 people

Question 2

Use algebraic procedures to find the exact solution(s)of the equation below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Use algebraic procedures to find the exact solution of the equation   .

Accepted Answer

A) -1, 13 
B)    
C)    
D) 1 
E)    
A) -1, 13 
B)    
C)    
D) 1 
E)

Question 4

The population of groundhogs on a ranch satisfies a logistic model in which   in the year 2004,   , and   . Calculate a logistic model to predict the size of the groundhog population in 2008.

Accepted Answer

A) 4600 
B) 59 
C) 710 
D) 700 
E) 630 
A) 4600 
B) 59 
C) 710 
D) 700 
E) 630

Question 5

The population of groundhogs on a ranch satisfies a logistic model in which   in the year 2004,   , and   . Determine the logistic model for this population, where t is the number of years after 2004.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Determine which of the following functions is graphed below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

The population P of a city grows exponentially according to the function   where t is measured in years. When, to the nearest year, will the population reach 15,000?

Accepted Answer

A) in 5.5 years 
B) in 8 years 
C) in 3 years 
D) in 12 years 
E) in 10 years 
A) in 5.5 years 
B) in 8 years 
C) in 3 years 
D) in 12 years 
E) in 10 years

Question 8

Write the equation below in its exponential form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

The function   models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?

Accepted Answer

A) 29 words/min 
B) 64 words/min 
C) 28 words/min 
D) 29 words/min. 
E) 67 words/min 
A) 29 words/min 
B) 64 words/min 
C) 28 words/min 
D) 29 words/min. 
E) 67 words/min

Question 10

If $8000 is invested at an annual interest rate of 3.5% and compounded annually, find the balance after 9 years.

Accepted Answer

A) $11,679.76 
B) $8869.74 
C) $10,534.47 
D) $9501.49 
E) $10,903.18 
A) $11,679.76 
B) $8869.74 
C) $10,534.47 
D) $9501.49 
E) $10,903.18

Question 11

Assuming that   has an inverse function, if   find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Determine which of the following functions is graphed below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

The function   gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?

Accepted Answer

A) 1.58% 
B) 2.55% 
C) 2.06% 
D) 1.29% 
E)    % 
A) 1.58% 
B) 2.55% 
C) 2.06% 
D) 1.29% 
E)    %

Question 14

The demand d for a specific product, in items per month, is given by   where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $   .

Accepted Answer

A)    units 
B)    units 
C)    units 
D)    units 
E)    units 
A)    units 
B)    units 
C)    units 
D)    units 
E)    units

Question 15

Draw the graph of the inverse relation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

One estimate gives the world panda population as 3100 in the year 1980 and 730 in the year 2000. Find an exponential model for the data in order to predict the year in which the panda population will be reduced to 130.

Accepted Answer

A) 2023 
B) 2005 
C) 2024 
D) 2029 
E) 2014 
A) 2023 
B) 2005 
C) 2024 
D) 2029 
E) 2014

Question 17

The number of digits N in the expansion of   , where both b and x are positive integers, is   where   denotes the nearest integer less than or equal to   Find the number of digits in   .

Accepted Answer

A)    digits 
B)    digits 
C)    digits 
D)    digits 
E)    digits 
A)    digits 
B)    digits 
C)    digits 
D)    digits 
E)    digits

Question 18

Use the change-of-base formula to approximate the logarithm below. Round your answer to four decimal places.

Accepted Answer

A) -0.3365 
B) -0.4854 
C) -0.1682 
D) 0.8271 
E) 0.6099 
A) -0.3365 
B) -0.4854 
C) -0.1682 
D) 0.8271 
E) 0.6099

Question 19

For   , find   . State any restrictions on the domain of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

How long will it take $6500 to triple if it is invested at an annual interest rate of 8.5% compounded continuously? Round to the nearest year.

Accepted Answer

A) 24 years 
B) 8 years 
C) 65 years 
D) 16 years 
E) 13 years 
A) 24 years 
B) 8 years 
C) 65 years 
D) 16 years 
E) 13 years

The population P of a city grows exponentially according to the function where t is measured in years. Find the population at time .

Use algebraic procedures to find the exact solution(s)of the equation below.

Use algebraic procedures to find the exact solution of the equation .

The population of groundhogs on a ranch satisfies a logistic model in which in the year 2004, , and . Calculate a logistic model to predict the size of the groundhog population in 2008.

The population of groundhogs on a ranch satisfies a logistic model in which in the year 2004, , and . Determine the logistic model for this population, where t is the number of years after 2004.

Determine which of the following functions is graphed below.

The population P of a city grows exponentially according to the function where t is measured in years. When, to the nearest year, will the population reach 15,000?

Write the equation below in its exponential form.

The function models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?

If $8000 is invested at an annual interest rate of 3.5% and compounded annually, find the balance after 9 years.

Assuming that has an inverse function, if find .

Determine which of the following functions is graphed below.

The function gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?

The demand d for a specific product, in items per month, is given by where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $ .

Draw the graph of the inverse relation.

One estimate gives the world panda population as 3100 in the year 1980 and 730 in the year 2000. Find an exponential model for the data in order to predict the year in which the panda population will be reduced to 130.

The number of digits N in the expansion of , where both b and x are positive integers, is where denotes the nearest integer less than or equal to Find the number of digits in .

Use the change-of-base formula to approximate the logarithm below. Round your answer to four decimal places.

For , find . State any restrictions on the domain of .

How long will it take $6500 to triple if it is invested at an annual interest rate of 8.5% compounded continuously? Round to the nearest year.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

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Preliminary Concepts

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Exam 4: Exponential and Logarithmic Functions

The population P of a city grows exponentially according to the function where t is measured in years. Find the population at time .

Use algebraic procedures to find the exact solution(s)of the equation below.

Use algebraic procedures to find the exact solution of the equation .

The population of groundhogs on a ranch satisfies a logistic model in which in the year 2004, , and . Calculate a logistic model to predict the size of the groundhog population in 2008.

The population of groundhogs on a ranch satisfies a logistic model in which in the year 2004, , and . Determine the logistic model for this population, where t is the number of years after 2004.

Determine which of the following functions is graphed below.

The population P of a city grows exponentially according to the function where t is measured in years. When, to the nearest year, will the population reach 15,000?

Write the equation below in its exponential form.

The function models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?

If $8000 is invested at an annual interest rate of 3.5% and compounded annually, find the balance after 9 years.

Assuming that has an inverse function, if find .

Determine which of the following functions is graphed below.

The function gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?

The demand d for a specific product, in items per month, is given by where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $ .

Draw the graph of the inverse relation.

One estimate gives the world panda population as 3100 in the year 1980 and 730 in the year 2000. Find an exponential model for the data in order to predict the year in which the panda population will be reduced to 130.

The number of digits N in the expansion of , where both b and x are positive integers, is where denotes the nearest integer less than or equal to Find the number of digits in .

Use the change-of-base formula to approximate the logarithm below. Round your answer to four decimal places.

For , find . State any restrictions on the domain of .

How long will it take $6500 to triple if it is invested at an annual interest rate of 8.5% compounded continuously? Round to the nearest year.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters