kyle buys a car for $58,000. his car immediately starts depreciating, losing 23% of its value every year…

kyle buys a car for $58,000. his car immediately starts depreciating, losing 23% of its value every year. how much will the car be worth in 12 years? if necessary, round your answer to the nearest cent.

kyle buys a car for $58,000. his car immediately starts depreciating, losing 23% of its value every year. how much will the car be worth in 12 years? if necessary, round your answer to the nearest cent.

Answer

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. Here, $P=$58000$, $r = 0.23$, and $t = 12$.

Step2: Substitute the values into the formula

$A=58000\times(1 - 0.23)^{12}$. First, calculate $1-0.23 = 0.77$. Then, find $(0.77)^{12}$. Using a calculator, $(0.77)^{12}\approx0.03777$. Next, multiply by the initial value: $A = 58000\times0.03777$. $A=58000\times0.03777 = 2190.66$.

Answer:

$$2190.66$