doug bought a new car for $25,000. he estimates his car will depreciate, or lose value, at a rate of 20% per…

doug bought a new car for $25,000. he estimates his car will depreciate, or lose value, at a rate of 20% per year. the value of his car is modeled by the equation $v = p(1 - r)^t$, where $v$ is the value of the car, $p$ is the price he paid, $r$ is the annual rate of depreciation, and $t$ is the number of years he has owned the car. according to the model, what will be the approximate value of his car after $4\frac{1}{2}$ years?\n\n$2,500\n$9,159\n$22,827\n$23,791

doug bought a new car for $25,000. he estimates his car will depreciate, or lose value, at a rate of 20% per year. the value of his car is modeled by the equation $v = p(1 - r)^t$, where $v$ is the value of the car, $p$ is the price he paid, $r$ is the annual rate of depreciation, and $t$ is the number of years he has owned the car. according to the model, what will be the approximate value of his car after $4\frac{1}{2}$ years?\n\n$2,500\n$9,159\n$22,827\n$23,791

Answer

Answer:

B. $9,159

Explanation:

Step1: Identify the values

$P = 25000$, $r=0.2$, $t = 4.5$

Step2: Substitute into the formula

$V=P(1 - r)^t=25000\times(1 - 0.2)^{4.5}$

Step3: Calculate $(1 - 0.2)^{4.5}$

$(1 - 0.2)^{4.5}=0.8^{4.5}$. First, $0.8^{4.5}=0.8^{4}\times0.8^{0.5}$. $0.8^{4}=0.4096$, and $0.8^{0.5}=\sqrt{0.8}\approx0.8944$. Then $0.8^{4.5}\approx0.4096\times0.8944\approx0.36636$.

Step4: Calculate the value of the car

$V = 25000\times0.36636\approx9159$.