Question

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

$y = 220(1.09)^x$

growth
decay
growth % increase
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Explanation:

Step1: Identify growth/decay factor

The exponential function is in the form $y = a(1+r)^x$, where $1+r$ is the base. Here, the base is $1.09$. Since $1.09 > 1$, this is growth.

Step2: Calculate percentage rate

Subtract 1 from the base to find the rate:
$r = 1.09 - 1 = 0.09$
Convert to percentage: $0.09 \times 100 = 9\%$

Answer:

Growth, 9% increase