Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y = 28(1.01)^x
This exponential function represents growth because the base of the exponential term (1.01) is greater than 1.
To determine the percentage rate of increase, we can compare the initial value of y (28) to the value of y when x increases by 1 (28(1.01)).
First, calculate the value of y when x increases by 1:
y(1) = 28(1.01) = 28.28
Next, calculate the difference between y(1) and the initial value of y:
28.28 - 28 = 0.28
To find the percentage increase, divide the difference (0.28) by the initial value of y (28), and then multiply by 100 to get the percentage:
(0.28/28) * 100 = 1%
Therefore, the percentage rate of increase for this exponential function is 1%.