ExemplarPart A

Yes, Tyler is correct. The function is exponential and explanations will vary.

� An equation of the form xy ab� is an exponential function.� By generating the first few values of the function for 1, 2, 3, ...x � we get

the values 16, 12.8, 10.24, ...y � There is a constant percentage rate of change and this is a feature of an exponential function.

Part B

The number 16 represents the initial value of the machine (in thousands of dollars). The machine was valued at $16,000 when it was new.

Part C

The number 45

(or 80%) represents the “decay” rate of the machine’s value. The

machine is worth 80% of its previous year’s value. This rate is often called the rate of depreciation. So another way to express this relationship is to say that the machine loses 20% of its value per year—or depreciates 20% per year. Example: That number represents how much money is lost each year.

Part D

I sketched the graph of the function with at least two points identified. The y-intercept is (0, 16) and other points may include (1, 12.8), (2, 10.24), (3, 8.192), etc. I did not have to label the axes since they are given in the prompt.