Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y
=
16
(
1.059
)
x
y=16(1.059)
x
This represents growth at a rate of approximately 5.9%.
To determine whether the change represents growth or decay, we look at the base of the exponential function (1.059).
If the base is greater than 1, it represents growth (expansion).
If the base is less than 1, it represents decay (contraction).
In this case, the base is 1.059, which is greater than 1. Therefore, the change represents growth.
To determine the percentage rate of increase, we subtract 1 from the base (1.059) and multiply by 100.
Percentage rate of increase = (1.059 - 1) * 100 = 0.059 * 100 = 5.9%
So, the exponential function represents a 5.9% growth rate.