Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y, equals, 420, left bracket, 0, point, 7, 2, right bracket, to the power x
y=420(0.72)^x
The given exponential function is y = 420(0.72)^x.
To determine whether the change represents growth or decay, we need to look at the base of the exponential function. In this case, the base is 0.72. Since the base (0.72) is between 0 and 1, the change represents decay.
To determine the percentage rate of decrease, we need to find the value of (0.72) as a decimal and subtract it from 1. Then, we can convert this difference into a percentage.
1 - 0.72 = 0.28
To convert this into a percentage, we multiply it by 100:
0.28 * 100 = 28
Therefore, the exponential function represents a decay of 28%.