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) $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.008 x ^ { 2 }$

Question

Quizplus · Accepted Answer

To convert the profit equation to measure advertising expenditures in dollars, replace $x$ with $\frac{x}{100}$ because the original equation measures advertising in hundreds of dollars. Substituting $\frac{x}{100}$ into the original equation gives $P\left(\frac{x}{100}\right) = 70 - 20\left(\frac{x}{100}\right) + 0.8\left(\frac{x}{100}\right)^2$. Simplifying this results in $P\left(\frac{x}{100}\right) = 70 - \frac{x}{5} + 0.00008x^2$, which matches option D.

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

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