Question

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

$y = 33(0.492)^x$

growth
decay
growth % increase
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Explanation:

Step1: Identify base of exponent

The exponential function is in the form $y = a(b)^x$, where $b=0.492$.

Step2: Classify growth/decay

Since $0 < b < 1$, this is decay.

Step3: Calculate decay rate

Decay rate = $1 - b$
$\text{Decay rate} = 1 - 0.492 = 0.508$
Convert to percentage: $0.508 \times 100 = 50.8\%$

Answer:

Decay, 50.8% decrease