Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
$y = 38(1.09)^x$
answer attempt 1 out of 2
growth % increase submit answer
growth
decay

Explanation:

Step1: Compare to growth/decay form

The standard exponential form is $y = a(1+r)^x$ for growth, $y = a(1-r)^x$ for decay, where $a>0$, $r>0$.
Given $y = 38(1.09)^x$, so $1+r = 1.09$.

Step2: Identify growth/decay

Since $1.09 > 1$, this is growth.

Step3: Calculate percentage rate

Solve for $r$: $r = 1.09 - 1 = 0.09$. Convert to percentage: $0.09 \times 100 = 9\%$.

Answer:

Growth, 9% increase