Question

A car depreciates by 20% each year after it is purchased. The table below shows the value of the car over the first three years. 1 2 G Year Value of Car $12,000 $9600 $7680 a) Write an equation to represent this sequence. b) What will be the value of the car after 8 years?

Answer 1

The value of the car depreciates by 20% each ear, meaning after one year the price of the car is 80% of the original price.

In our case, the initial price of the car is $12,000; therefore after one year, its price will be

$12000\times\frac{80}{100}=12000\times0.8$

after 2 years

$(12000\times0.8)\times\frac{80}{100}=12000\times0.8\times0.8$

after three years

$12000\times0.8\times0.8\textcolor{#FF7968}{\times0.8}$

and therefore, after n years

$12000\times0.8^{n-1}$

Hence, after 8 years n= 8; therefore,

$12000\times0.8^7=2516.6$

To conclude, the value of the car after 8 years will be $2516.6.