a stereo is worth $7,438. it depreciates at a rate of 8% a year. what is its value after 10 years? round…

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation, and $t$ is the time in years.

Step2: Substitute the given values

Here, $P=$7438$, $r = 0.08$ (since $8%=0.08$), and $t = 10$. So, $A=7438\times(1 - 0.08)^{10}$.

Step3: Calculate the value inside the parentheses

$1-0.08 = 0.92$.

Step4: Calculate the power

$(0.92)^{10}\approx0.43438845$.

Step5: Multiply by the initial value

$A = 7438\times0.43438845\approx3220.98$.

Answer:

$$3220.98$