Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
( y = 90(1.02)^x )
answer attempt 1 out of 2
growth
% increase submit answer

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 $a>0$. Here, the base is $1.02>1$, so it is growth.

Step2: Solve for growth rate $r$

Set $1+r = 1.02$.
$r = 1.02 - 1 = 0.02$
Convert to percentage: $0.02 \times 100 = 2\%$

Answer:

Growth, 2% increase