Question

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

$y = 130(0.32)^x$

Explanation:

Step1: Identify growth/decay factor

The exponential function is in the form $y = a(b)^x$, where $b$ is the base. Here, $b = 0.32$. Since $0 < b < 1$, this is decay.

Step2: Calculate decay percentage

Subtract the base from 1 to find the decay rate, then convert to a percentage.
$1 - 0.32 = 0.68$, so the percentage is $0.68 \times 100 = 68\%$

Answer:

Decay, 68% decrease