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

Answer:

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

Step-by-step 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 $c(x) = 0.75\cdot e^{0.08\cdot x}+10$.