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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]
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]