Question

A car was purchased for $34,000. The car depreciates by 27% of each year

a) What is the value of the car when it is 12 years old?

b) How long will it take for the car to be worth less than $100?

Answer 1

Answer: a) $778.67  b) 19 years

Step-by-step explanation:

The formula you would use is

$a_{n}=P(1-r)^{n}$

where a is the amount

n is the length of time

P is the principle

and r is the rate in decimal form

a)

$a^{12} =34,000(1-.27)^{12} \\a_{12}=34,000(.73)^{12}\\a_{12} =778.67$

b)

put your initial equation into a graphing calculator and  use the table function to find that after 18 years it is worth 117 and in 19 years 86-