Chapter 3.1
Q. 3.1.1
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.
