Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Question

y= 21(0.97)^x

This is the exponential function

Answer 1

For any exponential function in which the base is less than 1, it will be an exponential decay situation. In this problem, the base is 0.97. The amount that the base is less than 1 ( i.e. 1 - base) represents, in decimal form, the percent of decrease, which in this case is 0.03 or 3%.

Answer 2

This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is .97 which is less than 1, representing decay.

The formula for exponential decay is y=a(1-r)^x.

r is the decay rate, expressed as a decimal.

In this case, r = .03 which represents 3%!