The Weekly Profit $P$ (In Hundreds of Dollars) for a Business from a Product

question 89

Multiple Choice

The weekly profit $P$ (in hundreds of dollars) for a business from a product is given by the model $P ( x ) = 70 - 20 x + 0.8 x ^ { 2 },$ $0 \leq x \leq 20$ where $x$ is the amount (in hundreds of dollars) spent on advertising. Rewrite the profit equation so that $x$ measures advertising expenditures in dollars.

• A) \(P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.8 x ^ { 2 }\)
• B) \(P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.00008 x ^ { 2 }\)
• C) \(P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.008 x ^ { 2 }\)
• D) \(P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.00008 x ^ { 2 }\)
• E) \(P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.008 x ^ { 2 }\)

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Definitions:

Social Cognitive Theory

A theoretical framework that emphasizes the importance of observational learning, imitation, and modeling in acquiring new behaviors.

Modelling

The representation or duplication of behaviors, attitudes, or physical attributes of individuals or systems, often used in learning or problem-solving contexts.

Partial Reinforcement

A conditioning process in which a reward or punishment is administered only some of the time after the desired behavior occurs, leading to stronger behavioral responses.

Delayed Reinforcement

A consequence that follows an action or behavior with a significant time gap, which can impact the strength and formation of the associated behavior.