Question

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

$y = 970(0.51)^x$

answer
attempt 1 out of 2
growth % increase
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Explanation:

Step1: Identify growth/decay factor

The general form of an exponential function is $y = a(b)^x$, where $b$ is the growth/decay factor. For $y = 970(0.51)^x$, $b = 0.51$. Since $0 < b < 1$, this is decay.

Step2: Calculate decay percentage

The percentage rate of decrease is found by $1 - b$.
$1 - 0.51 = 0.49$, which is $49\%$.

Answer:

Decay, 49% decrease