type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction…

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).\ncharlie runs a book - rental business. he currently charges $3 per book and rents out an average of 38 books a day. according to a study, for every 50¢ increase in rental price, the average business can expect to lose 4 rentals a day. complete the equation that models this scenario, where $b(x)$ is the revenue generated and $x$ is the number of 50¢ price increases.\n$b(x)=-square x^{2}+square x+square$

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).\ncharlie runs a book - rental business. he currently charges $3 per book and rents out an average of 38 books a day. according to a study, for every 50¢ increase in rental price, the average business can expect to lose 4 rentals a day. complete the equation that models this scenario, where $b(x)$ is the revenue generated and $x$ is the number of 50¢ price increases.\n$b(x)=-square x^{2}+square x+square$

Answer

Explanation:

Step1: Find the new price per book

The initial price per book is $3. For each $0.50 increase (represented by $x$), the new price per book $p(x)=3 + 0.5x$.

Step2: Find the number of books rented

The initial number of books rented is 38. For each $0.50 increase (represented by $x$), the number of books rented $n(x)=38-4x$.

Step3: Calculate the revenue function

Revenue $b(x)$ is the product of the price per - book and the number of books rented. So $b(x)=p(x)\times n(x)=(3 + 0.5x)(38-4x)$. Expand the right - hand side using the FOIL method: [ \begin{align*} b(x)&=3\times38+3\times(-4x)+0.5x\times38+0.5x\times(-4x)\ &=114-12x + 19x-2x^{2}\ &=-2x^{2}+7x + 114 \end{align*} ]

Answer:

-2, 7, 114