# Duru has an ice-cream stand, which she opens on days that are forecasted to be warmer than 10°C. When open for business, her daily pro

Question

Duru has an ice-cream stand, which she opens on days that are forecasted to be warmer than 10°C.
When open for business, her daily profit, P, is a function of the number of cones she sells, n, and can be
modeled by the function P(n) = 2n – 20. Additionally, she finds that the number of cones she sells, C.
is a function of the average temperature, t, in degrees Celsius (°C), and can be modeled by the function
C(t) = 50 + 10(t – 10).
Find an explicit expression that gives Duru’s profit on a day with an average temperature of t° C.

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1 year 2021-09-04T20:56:04+00:00 2 Answers 92 views 0

Step-by-step explanation:

[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]