Question

POINTS 20POINTS!!!

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

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

Explanation:

The average cost equation in the year 2005 is:

The average cost equation in the year 2010 is

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

We regroup the terms to get,

Combine the similar terms to

Answer 2

Remark

The difference is C_2005 - C_2010

Calculation

C_2005 - C_2010 = (-15x^2 + 20x - 3) - (- 10X^2 + 30x - 2) Remove the brackets

C_2005 - C_2010 = - 15x^2 +20x - 3 + 10^2 - 30x + 2 Look how the signs change in the second set of brackets.

C_2005 - C_2010 = -5x^2 - 10x - 1 Answer