The value of the new car purchased for $27600 depricates 10%per year.

Question

Write an exponential decay model for the value of the car.After about how many years will the car be worth half of its purchase price?

Answer 1

Value in one year = 27600 - 0.10(27600)=27600(1-0.10)

                                                                      = 27600(0.90)

 

Value in 2 years = 27600(0.90) - 0.10(27600)(0.90)

                            = 27600(0.90)(1 - 0.10)

                            = 27600(0.90)²

 

Value in n years = 27600(0.90)ⁿ

 

 

27600(0.90)ⁿ = 13800

 

           (0.90)ⁿ = 0.5

 

       log(0.90)ⁿ = log(0.5)

 

     nlog(0.90) = log(0.5)     So, n = log(0.5)/log(0.90)

                                                     n = 6.5788 years

 

The car will be worth half of its original value in about 

6.6 years.