Question

In the year 2005, the average cost of a car could be modeled by the equation C= -15x2 + 20x - 3 where x is the number of years since 2005. By the year 2010 the average cost had changed, and the equation could be modeled by C= -10x2 + 30x - 2. Find the difference in average cost equation for cars between 2005 and 2010.

Answer 1

Thank you kudzordzifrancis

Step-by-step explanation: His answer is right! Sorry I need the points for an exam I don't understand. :(

Answer 2

`C_(2010) - C_(2005) = 5 {x}^(2)+ 10x + 1`

Step-by-step explanation

The average cost equation in the year 2005 is:

`C_(2005)</p><p>= - 15 {x}^(2) + 20x - 3`

The average cost equation in the year 2010 is

`C_(2010)</p><p>= - 10 {x}^(2) + 30x - 2`

The difference in average cost equation for cars between 2005 and 2010 is

`C_(2010) - C_(2005) = - 10 {x}^(2) + 30x - 2 - ( - 15 {x}^(2) + 20x - 3)`

`C_(2010) - C_(2005) = - 10 {x}^(2) + 30x - 2 + 15 {x}^(2) - 20x + 3`

We regroup the terms to get,

`C_(2010) - C_(2005) = - 10 {x}^(2) + 15 {x}^(2)+ 30x - 20x + 3 - 2`

Combine the similar terms to

`C_(2010) - C_(2005) = 5 {x}^(2)+ 10x + 1`