Question

depreciation the value of a home theater system depreciates by about 7% each year. aeryn purchases a home theater system for $3000. what is its value 4 years after purchase? round your answer to the nearest hundred.

Explanation:

Step1: Define depreciation formula

The formula for exponential depreciation is $V = P(1-r)^t$, where $P=\$3000$, $r=0.07$, $t=4$.

Step2: Calculate remaining value factor

$1-r = 1-0.07 = 0.93$

Step3: Compute factor raised to time

$0.93^4 \approx 0.748052$

Step4: Find final value

$V = 3000 \times 0.748052 \approx 2244.16$

Step5: Round to nearest hundred

Round $2244.16$ to the nearest hundred, which is $2200$.

Answer:

$\$2200$