Question

Duru has an ice-cream stand, which she opens on days that are forecasted to be warmer than 10°C.

Answer 1

Answer:

$P(c(t)) = 20t-120$

Step-by-step explanation:

Given

$P(n) = 2n - 20$

$C(t) = 50 + 10(t - 10)$

Required

Determine $P(C(t))$

The implication of the question is to solve for $P(C(t))$

Given that

$C(t) = 50 + 10(t - 10)$ and $P(n) = 2n - 20$

$P(c(t))$ would be

$P(c(t)) = 2(50 + 10(t - 10)) - 20$

$P(c(t)) = 2(50 + 10t - 100) - 20$

Collect Like Terms

$P(c(t)) = 2(50 - 100+ 10t) - 20$

$P(c(t)) = 2(-50+ 10t) - 20$

Open Bracket

$P(c(t)) = -100+ 20t - 20$

Collect Like Terms

$P(c(t)) = 20t-100 - 20$

$P(c(t)) = 20t-120$