Question

Car dealers sometimes use the rule of thumb that a car loses about 30% of its value each year. 1. Suppose you bought a new car in December 2010 for $15,000. 2. Develop a general formula for the value of the car t years after its purchase. HELP

Answer 1

Answer: $A=15000(1.30)^t$

Step-by-step explanation:

Formula to find the price of an item after t years after withe a depreciation rate of r% is $A=P(1-\dfrac{r}{100})^t$, where P = Initial value of item.

Given: P = $15,000, r= 30%

Then, the value of car after t years will be :

$A= 15000(1+\dfrac{30}{100})^t\\\\\Rightarrow\ A=15000(1+0.30)^t\\\\\Rightarrow\ A=15000(1.30)^t$

The required general formula for the value of the car t years after its purchase:

$A=15000(1.30)^t$