10. an investment of $8200 loses value at a rate of 2% per year. write an exponential decay function to find…

Explanation:

Step1: Identify decay - formula

The general form of an exponential decay function is $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time in years.

Step2: Determine values of $a$, $r$, and $t$

Given that $a=$8200$, $r = 0.02$ (since $2%=0.02$), and $t = 9$.

Step3: Substitute values into formula

The exponential - decay function is $y=8200(1 - 0.02)^9$.

Step4: Calculate the value

First, calculate $1-0.02 = 0.98$. Then, find $(0.98)^9\approx0.83374$. Multiply by $8200$: $y = 8200\times0.83374\approx6836.67$.

Answer:

The exponential decay function is $y = 8200(0.98)^9$, and the value of the investment after 9 years is approximately $$6836.67$.