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## 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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Mathematics
1 year
2021-09-04T20:56:04+00:00
2021-09-04T20:56:04+00:00 2 Answers
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## Answers ( )

Answer:20t-120 is the correct answer.

Step-by-step explanation: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]

RequiredDetermine [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]