8 In the year 2012 Anna bought a new car for 26000 In 2017 s

8. In the year 2012, Anna bought a new car for $26,000. In 2017, she was told that the value of her car was $15,000 due to depreciation. She is told that the value of the car depreciates linearly a. Find a function V(t) which gives the value of the car t years after the year 2010. b. Find the value of the car in 2012, and 2015

Solution

There seems to be an error here. It appears that the car was purchased in 2010 and not in 2012( because, otherwise, there would not be anypoint in asking for the value of the car in 2012. Also, the value of the car t years after 2010 would be indeterminate.

8. The depreciation in the value of Anna’s car is a linear function. From $ 26000 in 2010, the value of the car depreciates to $ 15000 in 2017, i.e. by $ 26000-$ 15000 = $ 11000 in 7 years. Thus, the depreciation in the value of Anna’s car is $ 11000/7( = $1571.43 approximately, on rounding off to the nearest cent) per year.

a. If V(t) is the value of the car t years after 2010, then V(t) = 26000-(11000/7)t.

b. The value of the car in 2012 will be 26000-(11000/7)*2 = 26000-3142.86 = $ 22857.14. The value of the car in 2015 will be 26000-(11000/7)*5 = 26000-7857.14 = $ 18142.86.