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Chapter 3.1

Q. 3.1.1

Evaluating an Exponential Function

The exponential function f(x)=42.2(1.56)^x models the average amount spent, f(x), in dollars, at a shopping mall after x hours. What is the average amount spent, to the nearest dollar, after four hours?

Step-by-Step

Verified Solution

Because we are interested in the amount spent after four hours, substitute 4 for x and evaluate the function.

f(x)=42.2(1.56)^x                  This is the given function.

f(4)=42.2(1.56)^4                  Substitute 4 for x.

Use a scientific or graphing calculator to evaluate f(4). Press the following keys on your calculator to do this:

Scientific calculator:    42.2 \fbox{×} 1.56  y^{x} 44 \fbox{=}

Graphing calculator:  42.2 \fbox{×} 1.56 \fbox{∧} 4 \fbox{ENTER}.

The display should be approximately 249.92566.

f(4)=42.2(1.56)^4 \approx 249.92566 \approx 250

Thus, the average amount spent after four hours at a mall is $250.

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