Q:

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=8700(1.04)^4 ​​

Accepted Solution

A:
We are given this function:
[tex]y=8700* (1.04)^{4} [/tex]

8700 is the initial amount.
1.04 shows the change of original amount. This is decimal form of percentage. We need to transform it into regular percentage.
1.04 * 100% = 104%
Now we observe this number. If it is greater than 100% we have growth, if it is lower than 100% it is decay, and if it is equal to 100% than there is no change.
In our case this number is greater than 100% so we have growth. To determine the percentage rate we must substract 100% as it represents the original amount.
104% - 100% = 4%
This would be our solution if we don't have an exponent.

We have exponent so first step is to calculate the number and then we repeat the steps from above.
[tex] 1.04^{4} = 1,16985856[/tex]
1,16985856 * 100% β‰ˆ 116,99%
116.99% - 100% = 16.99%
So, final solution is growth of 16.99%