Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
$y = 5800(0.806)^x$

Explanation:

Step1: Identify growth/decay

The general exponential form is $y = a(b)^x$. If $0 < b < 1$, it is decay. Here, $b=0.806$, so it is decay.

Step2: Calculate decay rate

Subtract $b$ from 1 to find the decay rate: $1 - 0.806 = 0.194$. Convert to percentage: $0.194 \times 100 = 19.4\%$.

Answer:

Decay, 19.4% decrease