Question
Find an expression that gives the amount by which the revenue of the second gas station will exceed the revenue of the first gas station in month $t(0 \leq t \leq 12)$.
Step 1
The first gas station has a revenue model of $0.2t^2 + 150t$, and the second gas station has a revenue model of $0.5t^2 + 200t$. Show more…
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Refer to Exercise $141 .$ Find an expression that gives the amount by which the revenue of the second gas station will exceed the revenue of the first gas station in month $t(0 \leq t \leq 12)$.
Preliminaries
Precalculus Review I
Jake owns two gas stations. The total revenue of the first gas station for the next 12 months is projected to be $$0.2 t^{2}+150 t \quad(0 \leq t \leq 12)$$ thousand dollars $t$ months from now. The total revenue of the second gas station for the next 12 months is projected to be $$0.5 t^{2}+200 t \quad(0 \leq t \leq 12)$$ thousand dollars $t$ months from now. Find an expression that gives the total revenue realized by Jake's gas stations in month $t(0 \leq t \leq 12)$.
Suppose a local vendor charges $\$ 2$ per hot dog and that the number of hot dogs sold per hour $x$ is given by $x(t)=-4 t^{2}+20 t+92,$ where $t$ is the number of hours since 10 AM, $0 \leq t \leq 4$. (a) Find an expression for the revenue per hour $R$ as a function of $x .$ (b) Find and simplify $(R \circ x)(t) .$ What does this represent? (c) What is the revenue per hour at noon?
Further Topics in Functions
Function Composition
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