Question

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 $t(0 \leq t \leq 12)$.

Name: Problem 141, Chapter 1: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-14T14:32:35-08:00
Duration: 1 min 12 s
Channel: Christopher Stanley

   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 $t(0 \leq t \leq 12)$.

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 1, Problem 141

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Solved by Expert Christopher Stanley

05/14/2021

Step 1

The revenue for the first gas station is given by the expression $0.2t^2 + 150t$ thousand dollars. The revenue for the second gas station is given by the expression $0.5t^2 + 200t$ thousand dollars. Show more…

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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 $t(0 \leq t \leq 12)$.

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Key Concepts

Domain Considerations

The domain of a function refers to the set of all possible input values for which the function is defined. When combining functions, it is important to consider the domain constraints of the individual functions to ensure that the resulting function correctly represents the scenario over the intended interval.

Polynomial Functions

Polynomial functions are expressions consisting of variables raised to non-negative integer powers, multiplied by coefficients, and summed together. When adding polynomial functions, like terms—terms with the same power of the variable—are combined to simplify the expression.

Function Addition

Function addition involves combining two functions by adding their corresponding outputs for each value in the domain. This technique is used to create a new function that represents the total effect or combined quantity represented by the original functions.

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