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. 4 years c. 6 years d. 2 years

Explanation:

Step1: Set up the depreciation formula

The formula for exponential - decay (depreciation) is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of depreciation, and $t$ is the number of years. Here, $P=\$1875$, $r = 0.2$, and $A=\$768$. So the equation becomes $768=1875(1 - 0.2)^t$.

Step2: Simplify the equation

First, simplify $(1 - 0.2)$ to $0.8$. The equation is $768 = 1875\times0.8^t$. Then, divide both sides of the equation by $1875$: $\frac{768}{1875}=0.8^t$. Calculate $\frac{768}{1875}=0.4096$. So, $0.4096 = 0.8^t$.

Step3: Solve for $t$

Since $0.4096=0.8^4$ (because $0.8\times0.8\times0.8\times0.8 = 0.4096$), then $t = 4$.

Answer:

B. 4 years