MATH Basic Algebra II  - Unit 17: Exponential Growth and Decay
Some activities may require making graphs on paper.  Click here to view and print graph paper, as needed.

Exponential Functions

In the following problems, determine whether the function represents exponential growth or exponential decay by examining the multiplier.

1) The exponential function is what type?

2) The exponential function is what type?

In the following problems, evaluate the expression to the nearest thousandth for the given value of x.

3) Evaluate. Express the answer to the nearest thousandth.

Hint:  Remember that the nearest thousandth means there are 3 decimal places after the decimal point.

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4) Evaluate.  Express the answer to the nearest thousandth.
 
Hint:  Be sure to calculate the value for the exponent first.

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5) Evaluate.  Express the answer to the nearest thousandth.
 
Hint:  Be sure to calculate the value for the exponent first.

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Graphing Exponential Functions

In the next four questions, refer to the four graphs shown below.

6) Which graph matches the function?
 
Hint:  Make a table of values.  Choose x-values and substitute the values in the function and calculate y.
 
Click here to view the four choices.

7) Which graph matches the function?
 
Click here to view the four choices.

8) Which graph matches the function?
 
Click here to view the four choices.

9) Which graph matches the function?
 
Click here to view the four choices.

10) What is the x-intercept of the given function?

In the following problems, determine the y-intercept.
 
Hint:  Recall that the x-coordinate of the y-intercept is zero; thus, let x = 0 and solve.

11) What is the y-intercept of the given function?

12) What is the y-intercept of the given function?

13) Describe the range of the given function with the restrictions on the base (b).
 
Hint:  Assign b any value between 0 and 1, and graph.  Try a couple of different numbers and look for an overall pattern or trend in the range values.

Applications of Exponential Growth and Decay

In the following problems, find the multiplier for the rate of exponential growth or decay. Express the multiplier as a decimal.

14) What is the multiplier for a 1% exponential growth?

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15) What is the multiplier for a 7% exponential decay?

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16) What is the multiplier for a 5.2% exponential decay?

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17) What is the multiplier for a 7.5% exponential growth?

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In the next group of problems, exponential growth and exponential decay will be applied to real world scenarios.  Recall the basic formula:

In the following problems, predict the population based on the following scenario:

18) Based on the 4% growth rate, predict the population for the year 2020.
 
Hint:  Determine the initial population (a), the multiplier based on the growth rate (b), the time interval in decades (n), and then solve.  Note:  One decade = 10 years

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19) Based on the 4% growth rate, predict the population for the year 2025.
 
Note:  One decade equals 10 years; therefore, 5 years equals what part of a decade?

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20) Suppose you buy a car for $24,000 and that its value decreases by 20% per year. Predict the value of the car to the nearest dollar after 5 years.
 
Hint:  Determine the initial value (a), the multiplier (b), and the time interval in years (n), and then solve.

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21) The population of a city in 2010 was 50,000 and is decreasing at the rate of 1.5% per year.  Predict the population of the city to the nearest whole number in the year 2020.
 
Hint:  Determine the initial value (a), the multiplier (b), and the time interval in years (n), and then solve.

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In the following problems, calculate the final amount the investment will return through compound interest for the given terms.

22) What is the final amount of a $720 investment earning 6.2% interest compounded semiannually for 5 years?
 
Hint:  Determine the initial amount (P), the rate of earning (r), the number of times the interest is compounded per year (n), the time in years (t), and then solve.

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23) What is the final amount of a $300 investment earning 4.5% interest compounded quarterly for 3 years?

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Review

24) Solve the equation for x.
 
Hint:  Use cross products to solve.
 
Click here to review the unit content explanation for Solving Equations and Applications.

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25) Solve the equation for x.
 
Hint:  Apply the distributive property to eliminate the parenthesis.
 
Click here to review the unit content explanation for Solving Equations and Applications.

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26) Solve the inequality for x.
 
Hint:  Eliminate the fraction by multiplying both sides by 3.
 
Click here to review the unit content explanation for Inequalities and Absolute Value Equations.

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27) Evaluate.
 
Click here to review the unit content explanation for Operations with Numbers and Exponents.

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28) Multiply the matrices.
 
Hint:  Determine the dimensions of the product matrix, and then proceed to work row over each column.
 
Click here to review the unit content explanation for Matrices.

29) Show that the given function is a quadratic function by writing it in the standard form. 
 
Hint:  Use the FOIL property to multiply the two binomials.
 
Click here to review the unit content explanation for Quadratic Functions.

30) Solve using the quadratic formula.
 
Hint:  Put the quadratic equation in standard form, and then use the quadratic formula.
 
Click here to review the unit content explanation for Solving Quadratic Equations.

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