Question

You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually. Describe and correct the error in finding the value of the car in 2015.

v(t) = 25,000(1.14)^x
v(5) = 25,000(1.14)^5 = 48,135
The value of the car in 2015 is about $48,000.
Part A: Describe the error

Answer 1

The error in finding the value of the car in 2015 lies in the use of an incorrect formula. The correct formula should be v(t) = 25,000(1-0.14)^x. The value of the car in 2015 is approximately $20,506.

Step-by-step explanation:

The error in finding the value of the car in 2015 lies in the use of an incorrect formula. Currently, the given formula is:

v(t) = 25,000(1.14)^x

This formula is incorrect because it assumes that the value of the car is increasing by 14% annually, instead of decreasing. To correct the error, we need to use the correct formula, which should be:

v(t) = 25,000(1-0.14)^x

Using this corrected formula, we can find the value of the car in 2015, which is approximately $20,506.