Question

select the correct answer. cameron purchased an electric guitar for $1,875. the value of the guitar depreciates by 20% each year. in how many years will the guitar be valued at $768? a. 7 years b. 2 years c. 6 years d. 4 years

Explanation:

Step1: Define depreciation formula

The value after $n$ years is $V(n) = V_0(1-r)^n$, where $V_0=\$1875$, $r=0.20$, $V(n)=\$768$.

Step2: Substitute known values

$768 = 1875(1-0.20)^n$
$768 = 1875(0.8)^n$

Step3: Isolate the exponential term

$\frac{768}{1875} = 0.8^n$
$0.4096 = 0.8^n$

Step4: Solve for $n$ using logs

Take $\log$ of both sides: $\log(0.4096) = n\log(0.8)$
$n = \frac{\log(0.4096)}{\log(0.8)}$
$n = 4$

Answer:

D. 4 years