Question

The function C(x) = -2x2 + 38x + 40 models the sales, in hundreds of

millions of dollars, of compact discs for years since 1990.

Answer 1

Question:

Rewrite the function to reveal when sales of compact discs and $0.

Answer:

The cost in 2010 is $0

Explanation:

Given

`C(x) = -2x^2 + 38x + 40`

Required

Find x when
`C(x) = 0`

This gives:

`C(x) = -2x^2 + 38x + 40`

`-2x^2 + 38x + 40=0`

Expand

`-2x^2 + 40x -2x+ 40=0`

Factorize:

`-2x(x - 20) -2(x- 20)=0`

`(-2x - 2)(x- 20)=0`

Solve for x

`-2x-2=0\ or\ x - 20 = 0`

`x = -1\ or\ x = 20`

x represents time. So, it cannot be negative.

`x = 20`

20 years after 1990 is: 2010. Hence, the cost in 2010 is $0