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.

Respuesta :

ANSWER

[tex]C_{2010} - C_{2005} = 5 {x}^{2}+ 10x + 1[/tex]

EXPLANATION

The average cost equation in the year 2005 is:

[tex]C_{2005}

= - 15 {x}^{2} + 20x - 3[/tex]

The average cost equation in the year 2010 is

[tex]C_{2010}

= - 10 {x}^{2} + 30x - 2[/tex]

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

[tex]C_{2010} - C_{2005} = - 10 {x}^{2} + 30x - 2 - ( - 15 {x}^{2} + 20x - 3)[/tex]

[tex]C_{2010} - C_{2005} = - 10 {x}^{2} + 30x - 2 + 15 {x}^{2} - 20x + 3[/tex]

We regroup the terms to get,

[tex]C_{2010} - C_{2005} = - 10 {x}^{2} + 15 {x}^{2}+ 30x - 20x + 3 - 2[/tex]

Combine the similar terms to

[tex]C_{2010} - C_{2005} = 5 {x}^{2}+ 10x + 1[/tex]

Answer:

Thank you  kudzordzifrancis

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