Question 1

Which answer choice is a graph of the function? ​   ​

Accepted Answer

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

Question 2

Suppose that the equation   represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places. ​

Accepted Answer

A) after 3.66 years 
B) after 4.30 years 
C) after 100.00 years 
D) after 0.22 year 
E) after 1.12 years 
A) after 3.66 years 
B) after 4.30 years 
C) after 100.00 years 
D) after 0.22 year 
E) after 1.12 years

Question 3

A starfish population can be modeled by   , where   is the number of individuals at time   ,   is the yearly rate of growth, and t is the number of years. Sketch the graph for   to   when the growth rate is 2.3% and   is 2.5 billion. All numbers on the vertical axis are in billions.

Accepted Answer

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

Question 4

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation ​   .
​
Graph this equation for   .
​

Accepted Answer

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

Question 5

Suppose the supply of x units of a product at price p dollars per unit is given by   . How many units would be supplied when the price is $60 each? Round your answer to one decimal place. ​

Accepted Answer

A) 14,680.3 units 
B) 5,769,258.3 units 
C) 54,249.6 units 
D) 7,342.2 units 
E) 7,340.2 units 
A) 14,680.3 units 
B) 5,769,258.3 units 
C) 54,249.6 units 
D) 7,342.2 units 
E) 7,340.2 units

Question 6

Write the equation in exponential form. ​   ​

Accepted Answer

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

Question 7

On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by   , where y is the total number infected at time t (in days). How many are infected after 8 days? ​

Accepted Answer

A) approximately 52 students 
B) approximately 10 students 
C) approximately 9,987 students 
D) approximately 2,158 students 
E) approximately 3,038 students 
A) approximately 52 students 
B) approximately 10 students 
C) approximately 9,987 students 
D) approximately 2,158 students 
E) approximately 3,038 students

Question 8

Use a calculator to determine whether expression (a) is equivalent to expression (b). ​     ​

Accepted Answer

A) equivalent 
B) not equivalent 
A) equivalent 
B) not equivalent

Question 9

The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers. Find an equation that models these data and use it to predict the consumer price index in 2015. Use the model to predict the consumer price index in 2015. Round your answer to two decimal places. ​   ​
Source: U.S. Bureau of the Census
​

Accepted Answer

A) 76.47 
B) 129.14 
C) 169.33 
D) 216.39 
E) 326.77 
A) 76.47 
B) 129.14 
C) 169.33 
D) 216.39 
E) 326.77

Question 10

The securities industry experienced dramatic growth in the last two decades of the 20th century. The following models for the industry's revenue R and expenses or costs C (both in billions of dollars) were developed as functions of the years past 1980 with data from the U.S. Securities and Exchange Commission's 2000 Annual Report (2001).   and   . Use the models to predict the profit for the securities industry in 2009. Round your answer to two decimal places. ​

Accepted Answer

A) $1.15 billion 
B) $955.65 billion 
C) $830.61 billion 
D) $125.04 billion 
E) $540.34 billion 
A) $1.15 billion 
B) $955.65 billion 
C) $830.61 billion 
D) $125.04 billion 
E) $540.34 billion

Question 11

Suppose that the equation   represents the number of employees working t years after a company begins operations. How many employees are there when the company opens (at   )? ​

Accepted Answer

A) 4 employees 
B) 200 employees 
C) 10 employees 
D) 1 employee 
E) 12 employees 
A) 4 employees 
B) 200 employees 
C) 10 employees 
D) 1 employee 
E) 12 employees

Question 12

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with   ) is given by the equation   How long does it take for the concentration to reach 90? Round your answer to two decimal places. ​

Accepted Answer

A) ​4.98 hours 
B) 2.98 hours 
C) ​0.23 hour 
D) ​1.39 hours 
E) ​100.00 hours 
A) ​4.98 hours 
B) 2.98 hours 
C) ​0.23 hour 
D) ​1.39 hours 
E) ​100.00 hours

Question 13

For selected years from 1978 to 2002, the number of mutual funds N, excluding money market funds, can be modeled by   , where t is the number of years past 1975 (Source: Investment Company Institute, Mutual Fund Fact Book (2003)). Use the model to estimate the number of mutual funds in 2001. Round your answer to the nearest whole number. ​

Accepted Answer

A) 8,912 
B) 192 
C) 10,604 
D) 7,220 
E) 412,923 
A) 8,912 
B) 192 
C) 10,604 
D) 7,220 
E) 412,923

Question 14

Is the function   a growth exponential or decay exponential? ​

Accepted Answer

A) growth exponential 
B) decay exponential 
A) growth exponential 
B) decay exponential

Question 15

Solve for x by writing the equation in exponential form. Round your answer to two decimal places, if necessary. ​   ​

Accepted Answer

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

Question 16

Write the equation in logarithmic form. ​   ​

Accepted Answer

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

Question 17

Use the formula   . ​
The San Francisco earthquake of 1906 measured 8.25 on the Richter scale, and the San Francisco earthquake of 1989 measured 7.1. How much more intense was the 1906 quake?
​

Accepted Answer

A) 0.3 times as severe. 
B) 1.5 times as severe 
C) 5.7 times as severe 
D) 10.8 times as severe 
E) 14.1 times as severe 
A) 0.3 times as severe. 
B) 1.5 times as severe 
C) 5.7 times as severe 
D) 10.8 times as severe 
E) 14.1 times as severe

Question 18

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to   . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar. ​

Accepted Answer

A) $260,683 
B) $190,280 
C) $115,410 
D) $156,191 
E) $95,141 
A) $260,683 
B) $190,280 
C) $115,410 
D) $156,191 
E) $95,141

Question 19

Given   , use a graphing calculator to graph   for   and   . ​

Accepted Answer

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

Question 20

If the total cost function for a product is   , where x is the number of items produced, what is the total cost of producing 50 units? Round your answer to the nearest cent. ​

Accepted Answer

A) $812.01 
B) $948.41 
C) $52.23 
D) $801.65 
E) $813.59 
A) $812.01 
B) $948.41 
C) $52.23 
D) $801.65 
E) $813.59

Which answer choice is a graph of the function?

Suppose that the equation represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places.

A starfish population can be modeled by , where is the number of individuals at time , is the yearly rate of growth, and t is the number of years. Sketch the graph for to when the growth rate is 2.3% and is 2.5 billion. All numbers on the vertical axis are in billions.

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation . Graph this equation for .

Suppose the supply of x units of a product at price p dollars per unit is given by . How many units would be supplied when the price is $60 each? Round your answer to one decimal place.

Write the equation in exponential form.

On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by , where y is the total number infected at time t (in days). How many are infected after 8 days?

Use a calculator to determine whether expression (a) is equivalent to expression (b).

Suppose that the equation represents the number of employees working t years after a company begins operations. How many employees are there when the company opens (at )?

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation How long does it take for the concentration to reach 90? Round your answer to two decimal places.

Is the function a growth exponential or decay exponential?

Solve for x by writing the equation in exponential form. Round your answer to two decimal places, if necessary.

Write the equation in logarithmic form.

Use the formula . The San Francisco earthquake of 1906 measured 8.25 on the Richter scale, and the San Francisco earthquake of 1989 measured 7.1. How much more intense was the 1906 quake?

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar.

Given , use a graphing calculator to graph for and .

If the total cost function for a product is , where x is the number of items produced, what is the total cost of producing 50 units? Round your answer to the nearest cent.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 6: Exponential and Logarithmic Functions

Which answer choice is a graph of the function? ​ ​

Suppose that the equation represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places. ​

A starfish population can be modeled by , where is the number of individuals at time , is the yearly rate of growth, and t is the number of years. Sketch the graph for to when the growth rate is 2.3% and is 2.5 billion. All numbers on the vertical axis are in billions.

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation ​ . ​ Graph this equation for . ​

Suppose the supply of x units of a product at price p dollars per unit is given by . How many units would be supplied when the price is $60 each? Round your answer to one decimal place. ​

Write the equation in exponential form. ​ ​

On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by , where y is the total number infected at time t (in days). How many are infected after 8 days? ​

Use a calculator to determine whether expression (a) is equivalent to expression (b). ​ ​

Suppose that the equation represents the number of employees working t years after a company begins operations. How many employees are there when the company opens (at )? ​

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation How long does it take for the concentration to reach 90? Round your answer to two decimal places. ​

Is the function a growth exponential or decay exponential? ​

Solve for x by writing the equation in exponential form. Round your answer to two decimal places, if necessary. ​ ​

Write the equation in logarithmic form. ​ ​

Use the formula . ​ The San Francisco earthquake of 1906 measured 8.25 on the Richter scale, and the San Francisco earthquake of 1989 measured 7.1. How much more intense was the 1906 quake? ​

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar. ​

Given , use a graphing calculator to graph for and . ​

If the total cost function for a product is , where x is the number of items produced, what is the total cost of producing 50 units? Round your answer to the nearest cent. ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Which answer choice is a graph of the function?

Suppose that the equation represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places.

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation . Graph this equation for .

Suppose the supply of x units of a product at price p dollars per unit is given by . How many units would be supplied when the price is $60 each? Round your answer to one decimal place.

Write the equation in exponential form.

On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by , where y is the total number infected at time t (in days). How many are infected after 8 days?

Use a calculator to determine whether expression (a) is equivalent to expression (b).

Suppose that the equation represents the number of employees working t years after a company begins operations. How many employees are there when the company opens (at )?

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation How long does it take for the concentration to reach 90? Round your answer to two decimal places.

Is the function a growth exponential or decay exponential?

Solve for x by writing the equation in exponential form. Round your answer to two decimal places, if necessary.

Write the equation in logarithmic form.

Use the formula . The San Francisco earthquake of 1906 measured 8.25 on the Richter scale, and the San Francisco earthquake of 1989 measured 7.1. How much more intense was the 1906 quake?

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar.

Given , use a graphing calculator to graph for and .

If the total cost function for a product is , where x is the number of items produced, what is the total cost of producing 50 units? Round your answer to the nearest cent.