Question

Find the cost function for the marginal cost function. C(x) =0.06 e 0.08x; fixed cost is $10 C(x)=_______

Answer 1

The cost function for
`C(x) = 0.06\cdot e^(0.08\cdot x)` is
`c(x) = 0.75\cdot e^(0.08\cdot x)+10`.

Explanation:

The marginal cost function (
`C(x)`) is the derivative of the cost function (
`c(x)`), then, we should integrate the marginal cost function to find the resulting expression. That is:

`c(x) = \int {C(x)} \, dx + C_(f)`

Where:

`C_(f)` - Fixed costs, measured in US dollars.

If we know that
`C(x) = 0.06\cdot e^(0.08\cdot x)` and
`C_(f) = \$\,10`, then:

`c(x) = 0.06\int {e^(0.08\cdot x)} \, dx + 10`

`c(x) = 0.75\cdot e^(0.08\cdot x)+10`

The cost function for
`C(x) = 0.06\cdot e^(0.08\cdot x)` is
`c(x) = 0.75\cdot e^(0.08\cdot x)+10`.