Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y
=
8900
(
1.362
)
x
y=8900(1.362)
x
This represents growth. The percentage rate of increase is 36.2%.
To determine whether the change represents growth or decay in the exponential function y = 8900(1.362)^x, we need to analyze the base of the exponential term.
In this case, the base of the term (1.362) is greater than 1. Therefore, it represents exponential growth.
To calculate the percentage rate of increase, we can subtract the initial amount (8900) from the new amount after one period and then divide by the initial amount. Finally, we multiply by 100 to express it as a percentage.
Let's calculate it step by step:
1. Calculate the new amount after one period (x = 1):
y(1) = 8900 * (1.362)^1
y(1) = 12128.8
2. Subtract the initial amount from the new amount:
12128.8 - 8900 = 3228.8
3. Divide the difference by the initial amount:
3228.8 / 8900 ≈ 0.3624
4. Multiply by 100 to express it as a percentage:
0.3624 * 100 ≈ 36.24%
So, the exponential function y = 8900(1.362)^x represents exponential growth with a percentage rate of increase of approximately 36.24%.