Question

John and his sister each bought a car in 2005. John's car cost $3,000 and is decreasing in value $150 per year. The value (V) of his sister's car x years after 200 given by the function (x) - 250x4,000. Which statement correctly compares the values of the cars from 2005 until 2017?

A. John's car always has less value than his sister's car.
B. John's car always has more value than his sister's car.
C.Johns car has less value than his sister's car after 2015.
D. Johns car has more value than his sister's car after 2015

Answer 1

After calculating the depreciation for both cars, it's clear that as of 2017, John's car, which is worth $1,200, holds more value than his sister's car, which is worth $1,000. Therefore, the correct comparison is that John's car has more value after 2015.

Step-by-step explanation:

To analyze the value of John and his sister's cars from 2005 to 2017, we must calculate the depreciation of both vehicles over the years. For John's car, which originally cost $3,000, the value decreases by $150 each year. His sister's car, on the other hand, has a value given by the function V(x) = 4000 - 250x for each year after 2005.

For John's car, using simple arithmetic, we can calculate the value for each year until 2017:

• Value in 2005 (initial): $3,000
• Value in 2017: $3,000 - ($150 times 12 years) = $3,000 - $1,800 = $1,200

Now let's consider the sister's car's value in 2017. The function's variable x represents the number of years after 2005. So for 2017, which is 12 years after 2005, her car's value is:

V(12) = 4000 - (250 times 12) = 4000 - 3000 = $1,000

Comparing both values in 2017:

• John's car value: $1,200
• His sister's car value: $1,000

Therefore, the correct statement is: D. John's car has more value than his sister's car after 2015.