Answer:
[tex]P(c(t)) = 20t-120[/tex]
Step-by-step explanation:
Given
[tex]P(n) = 2n - 20[/tex]
[tex]C(t) = 50 + 10(t - 10)[/tex]
Required
Determine [tex]P(C(t))[/tex]
The implication of the question is to solve for [tex]P(C(t))[/tex]
Given that
[tex]C(t) = 50 + 10(t - 10)[/tex] and [tex]P(n) = 2n - 20[/tex]
[tex]P(c(t))[/tex] would be
[tex]P(c(t)) = 2(50 + 10(t - 10)) - 20[/tex]
[tex]P(c(t)) = 2(50 + 10t - 100) - 20[/tex]
Collect Like Terms
[tex]P(c(t)) = 2(50 - 100+ 10t) - 20[/tex]
[tex]P(c(t)) = 2(-50+ 10t) - 20[/tex]
Open Bracket
[tex]P(c(t)) = -100+ 20t - 20[/tex]
Collect Like Terms
[tex]P(c(t)) = 20t-100 - 20[/tex]
[tex]P(c(t)) = 20t-120[/tex]