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Session 7 :
Homework

You've already seen examples of exponential growth. When you have an exponential function where the constant multiple between outputs is less than 1, you have a decreasing function. Instead of exponential growth, you have exponential decay. Here's an example:

The brightness of a light can be described with a unit called a lumen. A certain type of mirror reflects 3/5 of the light that hits it. Suppose a light of 2,000 lumens is shined on a series of several mirrors.

mirrors

Problem H1

Complete the table to indicate how much light would be reflected by each of the first three mirrors. (Mirror 0 represents the original light.)

Mirror number

 

Reflected light (lumens)

0

 

2000

1

 

2

 

3

 

 

show answers

 

Mirror number

 

Reflected light (lumens)

0

 

2000

1

 

1200

2

 

720

3

 

432

 

hide answers


 

Problem H2

Solution  

One mirror in the series reflects about 12 lumens of light. What mirror number is it? How did you find your answer?


 

Problem H3

Solution  

Which mirror number reflects about 1/10 the original amount of light? Does it depend on the starting amount of light?


 

Problem H4

Solution  

The graph below shows the amount of light reflected by another series of mirrors. The amount of light reflected by this type of mirror is different from the amount reflected by the other mirrors you investigated. The intensity of the light being shone on the first mirror is also different.

graph

a. 

What is the intensity of the light being shone on the first mirror?

b. 

How much light was reflected by the first mirror?

c. 

What fraction of light does the first mirror reflect?

d. 

Do the other mirrors reflect the same fraction of light? That is, does this graph show exponential decay?


 

Problem H5

Solution  

Suppose you have the function y = (1/5)x.

a. 

As the value of the inputs increases, what happens to the outputs?

b. 

Is this an exponential growth function, or an exponential decay function?

c. 

Will you ever get 0 as an output? Explain your answer.

d. 

Will you ever get negative numbers as outputs? Explain your answer.

e. 

How does your answer to (c) relate to Problems H1-H4?


 

Homework problems taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p.175-176. www.glencoe.com/sec/math

Next > Session 8: More Nonlinear Functions

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