Question

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 ​​

Answer 1

We are given this function:
$y=8700* (1.04)^{4}$

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.
$1.04^{4} = 1,16985856$
1,16985856 * 100% ≈ 116,99%
116.99% - 100% = 16.99%
So, final solution is growth of 16.99%

Answer 2

Using exponential function concepts, it is found that it represents growth of 4%.

Exponential function:

An exponential function is modeled by:

$y(t) = y(0)(1 + r)^t$

In which:

• y(0) is the initial value.

• r is the rate of change. If it is positive, it represents growth, and if it is negative, it represents decay.

In this problem, the equation is:

$y = 8700(1.04)^t$

Hence:

$1 + r = 1.04$

$r = 0.04$

Since r = 0.04 is positive, it represents a growth of 4%.

To learn more about exponential function concepts, you can take a look at https://brainly.com/question/24757163