Answer:
The cost function for [tex]C(x) = 0.06\cdot e^{0.08\cdot x}[/tex] is [tex]c(x) = 0.75\cdot e^{0.08\cdot x}+10[/tex].
Step-by-step explanation:
The marginal cost function ([tex]C(x)[/tex]) is the derivative of the cost function ([tex]c(x)[/tex]), then, we should integrate the marginal cost function to find the resulting expression. That is:
[tex]c(x) = \int {C(x)} \, dx + C_{f}[/tex]
Where:
[tex]C_{f}[/tex] - Fixed costs, measured in US dollars.
If we know that [tex]C(x) = 0.06\cdot e^{0.08\cdot x}[/tex] and [tex]C_{f} = \$\,10[/tex], then:
[tex]c(x) = 0.06\int {e^{0.08\cdot x}} \, dx + 10[/tex]
[tex]c(x) = 0.75\cdot e^{0.08\cdot x}+10[/tex]
The cost function for [tex]C(x) = 0.06\cdot e^{0.08\cdot x}[/tex] is [tex]c(x) = 0.75\cdot e^{0.08\cdot x}+10[/tex].
