a car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value…

a car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. how much will the car be worth in 9 years? if necessary, round your answer to the nearest cent.

a car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. how much will the car be worth in 9 years? if necessary, round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of decay, and $t$ is the time. Here, $P=$43330$, $r = 0.17$, and $t = 9$.

Step2: Substitute the values into the formula

$A=43330\times(1 - 0.17)^9$. First, calculate $1-0.17 = 0.83$. Then, find $(0.83)^9$. $(0.83)^9=0.83\times0.83\times\cdots\times0.83$ (9 times). Using a calculator, $(0.83)^9\approx0.21737$.

Step3: Calculate the final value

$A = 43330\times0.21737$. $A\approx43330\times0.21737 = 9417.6321\approx$9417.63$.

Answer:

$9417.63$