a new car sells for $25,000. the value of the car decreases by 15% each year. what is the approximate value…

a new car sells for $25,000. the value of the car decreases by 15% each year. what is the approximate value of the car 5 years after it is purchased? 25,000(1 - 0.15)^5, or approximately $11,093 25,000 - 1500(5), or approximately $17,500 25,000(0.15)^5, or approximately $18,984 25,000 - (100 - 15)(5), or approximately $24,575

a new car sells for $25,000. the value of the car decreases by 15% each year. what is the approximate value of the car 5 years after it is purchased? 25,000(1 - 0.15)^5, or approximately $11,093 25,000 - 1500(5), or approximately $17,500 25,000(0.15)^5, or approximately $18,984 25,000 - (100 - 15)(5), or approximately $24,575

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 decay, and $t$ is the time. Here, $P=$25000$, $r = 0.15$, and $t = 5$.

Step2: Substitute the values into the formula

$A=25000\times(1 - 0.15)^5=25000\times(0.85)^5$.

Step3: Calculate $(0.85)^5$

$(0.85)^5=0.85\times0.85\times0.85\times0.85\times0.85\approx0.4437$.

Step4: Calculate the value of the car

$A = 25000\times0.4437\approx11093$.

Answer:

$25,000(1 - 0.15)^5$, or approximately $$11,093$