Question

The number of skateboards that can be produced by a company can be represented by the function f(h) = 325h, where h is the number of hours. The total manufacturing cost for b skateboards is represented by the function g(b) = 0.008b2 + 8b + 100. Which function shows the total manufacturing cost of skateboards as a function of the number of hours?

Answer 1

g(f(h)) = 845h2 + 2,600h + 100

Explanation:

Answer 2

`g(f(h)) = 845h^2 + 2600h + 100`

Explanation:

*The function g(b) shows the cost per b produced skateboards.

*The function f(h) tells us the number of skateboards produced as a function of time.

To find a function that shows the manufacturing cost of skateboards produced as a function of the number of hours we must find g(f(h)).

That is, we must introduce the function f(h) within the function g(b), making b = f(h)

So:

`g(f(h)) = 0.008(f(h))^2 + 8(f(h)) + 100\\\\g(f(h)) = 0.008(325h)^2 + 8(325h) + 100`

Finally, the function wanted is:

`g(f(h)) = 845h^2 + 2600h + 100`