Exam 1: Functions and Change

You have $500 invested in an account earning 7.6% interest compounded annually. Suppose the interest rate were compounded monthly instead, that is you earned % interest each month. How much interest would you then earn for a year?

(Short Answer)

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Question 41

Write a formula representing the function that says: The area of a circle is proportional to the square of its radius.

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Question 42

Using base e and transformations, find a formula for the exponential function shown in the graph below.

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Question 43

Given the equation , find and simplify .

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Question 44

Use logarithms to solve the equation . Round to two decimal places.

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Question 45

The following graph shows the quantity of goods purchased by consumers at various prices. If the price is $15 per item, how many items do consumers purchase?

(Multiple Choice)

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Question 46

A. Which two lines in the following figure have the same slope? Enter your answer as "I and II," etc. B. Which two lines have the same y-intercept? C. Which line has the largest slope? D. Which line has the largest y-intercept?

(Short Answer)

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Question 47

The graphs of and are given in the following figure. Estimate .

(Multiple Choice)

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Question 48

Of the three functions below, one is a quadratic, one is a cubic, and one is a periodic function. Which one is h(x)?

(Multiple Choice)

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Question 49

Sketch global pictures of the functions , , and on the same set of axes. Label each function on both ends so it is obvious which is which.

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Question 50

A new music company wants to start selling collections of digital downloads. The profit (in thousands of dollars) is , where p is the price of a collection (in dollars). Use a graphing calculator to graph , and use the graph to answer the following. A. What is the maximum profit that can be obtained? B. What is the price of a collection of downloads when the maximum profit is obtained?

(Short Answer)

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Question 51

The elimination half-life of aspirin in plasma is estimated to be between 15 and 20 minutes. Assuming the lower estimate of 15 minutes, how long will it take a dose of 81 mg to decrease to ²/₃the original amount (54 mg) in the plasma?

(Multiple Choice)

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Question 52

Suppose $1200 is invested at 10% annual interest and $1500 is invested at 8% annual interest. After how many years will the investments be equal? Round to the nearest whole number.

(Short Answer)

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Question 53

Which is worth more after 10 years: $1200 invested at 10% annual interest or $1500 invested at 8% annual interest?

(Multiple Choice)

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Question 54

Use the function in the graph to complete the table of values.

(Short Answer)

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Question 55

Poiseuille's law says that the rate of flow, F, of a gas through a cylindrical pipe is proportional to the fourth power of the radius of the pipe, r. If the rate of flow is 400 cm³/sec in a pipe of radius 2 cm for a certain gas, how many cm³/sec flow through a pipe with a 6 cm radius? Round to 2 decimal places.

(Short Answer)

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Question 56

What is the doubling time of prices which are increased by 13% per year? Round to the nearest hundredth of a year.

(Short Answer)

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Question 57

The following table gives values for three different functions. Find a formula for the linear one.

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Question 58

What value of B would you use if was to model a periodic function, where t is measured in hours and the period is 1 day? Round to 4 decimal places.

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Question 59

Use the following table to find .

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Question 60

Showing 41 - 60 of 204

You have $500 invested in an account earning 7.6% interest compounded annually. Suppose the interest rate were compounded monthly instead, that is you earned % interest each month. How much interest would you then earn for a year?

Write a formula representing the function that says: The area of a circle is proportional to the square of its radius.

Using base e and transformations, find a formula for the exponential function shown in the graph below.

Given the equation , find and simplify .

Use logarithms to solve the equation . Round to two decimal places.

The following graph shows the quantity of goods purchased by consumers at various prices. If the price is $15 per item, how many items do consumers purchase?

A. Which two lines in the following figure have the same slope? Enter your answer as "I and II," etc. B. Which two lines have the same y-intercept? C. Which line has the largest slope? D. Which line has the largest y-intercept?

The graphs of and are given in the following figure. Estimate .

Of the three functions below, one is a quadratic, one is a cubic, and one is a periodic function. Which one is h(x)?

Sketch global pictures of the functions , , and on the same set of axes. Label each function on both ends so it is obvious which is which.

The elimination half-life of aspirin in plasma is estimated to be between 15 and 20 minutes. Assuming the lower estimate of 15 minutes, how long will it take a dose of 81 mg to decrease to ²/₃the original amount (54 mg) in the plasma?

Suppose $1200 is invested at 10% annual interest and $1500 is invested at 8% annual interest. After how many years will the investments be equal? Round to the nearest whole number.

Which is worth more after 10 years: $1200 invested at 10% annual interest or $1500 invested at 8% annual interest?

Use the function in the graph to complete the table of values.

What is the doubling time of prices which are increased by 13% per year? Round to the nearest hundredth of a year.

The following table gives values for three different functions. Find a formula for the linear one.

What value of B would you use if was to model a periodic function, where t is measured in hours and the period is 1 day? Round to 4 decimal places.

Use the following table to find .

Rate of Change: the Derivative

Shortcuts to Differentiation

Using the Derivative

Accumulated Change: the Definite Integral

Antiderivatives and Applications

Probability

Functions of Several Variables

Mathematical Modeling Using Differential Equations

Geometric Series

Filters

Exam 1: Functions and Change

You have $500 invested in an account earning 7.6% interest compounded annually. Suppose the interest rate were compounded monthly instead, that is you earned % interest each month. How much interest would you then earn for a year?

Write a formula representing the function that says: The area of a circle is proportional to the square of its radius.

Using base e and transformations, find a formula for the exponential function shown in the graph below.

Given the equation , find and simplify .

Use logarithms to solve the equation . Round to two decimal places.

The following graph shows the quantity of goods purchased by consumers at various prices. If the price is $15 per item, how many items do consumers purchase?

A. Which two lines in the following figure have the same slope? Enter your answer as "I and II," etc. B. Which two lines have the same y-intercept? C. Which line has the largest slope? D. Which line has the largest y-intercept?

The graphs of and are given in the following figure. Estimate .

Of the three functions below, one is a quadratic, one is a cubic, and one is a periodic function. Which one is h(x)?

Sketch global pictures of the functions , , and on the same set of axes. Label each function on both ends so it is obvious which is which.

The elimination half-life of aspirin in plasma is estimated to be between 15 and 20 minutes. Assuming the lower estimate of 15 minutes, how long will it take a dose of 81 mg to decrease to 2/3 the original amount (54 mg) in the plasma?

Suppose $1200 is invested at 10% annual interest and $1500 is invested at 8% annual interest. After how many years will the investments be equal? Round to the nearest whole number.

Which is worth more after 10 years: $1200 invested at 10% annual interest or $1500 invested at 8% annual interest?

Use the function in the graph to complete the table of values.

What is the doubling time of prices which are increased by 13% per year? Round to the nearest hundredth of a year.

The following table gives values for three different functions. Find a formula for the linear one.

What value of B would you use if was to model a periodic function, where t is measured in hours and the period is 1 day? Round to 4 decimal places.

Use the following table to find .

Rate of Change: the Derivative

Shortcuts to Differentiation

Using the Derivative

Accumulated Change: the Definite Integral

Antiderivatives and Applications

Probability

Functions of Several Variables

Mathematical Modeling Using Differential Equations

Geometric Series

Filters

The elimination half-life of aspirin in plasma is estimated to be between 15 and 20 minutes. Assuming the lower estimate of 15 minutes, how long will it take a dose of 81 mg to decrease to ²/₃the original amount (54 mg) in the plasma?