Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y
=
8600
(
0.11
)
x
y=8600(0.11)
x
This exponential function represents growth. The percentage rate of increase is 11%.
To determine whether the given exponential function represents growth or decay, we need to examine the value of the base, which is 0.11.
If the base (0.11) is between 0 and 1, the function represents decay because each time the exponent increases, the value of y decreases.
If the base is greater than 1, the function represents growth because each time the exponent increases, the value of y increases.
In this case, the base (0.11) is between 0 and 1, so the function represents decay.
To determine the percentage rate of decrease, we can subtract 1 from the base (0.11) and multiply by 100.
Percentage rate of decrease = (0.11 - 1) × 100 = (-0.89) × 100 = -89%
Therefore, the exponential function represents decay with a percentage rate of decrease of 89%.