Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\\(y = 9700(0.909)^x\\)

Explanation:

Step1: Identify growth/decay factor

The exponential function is in the form $y = a(b)^x$, where $b$ is the base. Here, $b = 0.909$, which is less than 1, so this is decay.

Step2: Calculate decay percentage

Subtract the base from 1 to find the rate:
$1 - 0.909 = 0.091$
Convert to percentage: $0.091 \times 100 = 9.1\%$

Answer:

Decay, 9.1% decrease