Question

Charlie 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 50C 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.

b(x)= x + x+ [

Answer 1

To model Charlie's book rental business revenue as a function of the price increases, the equation is b(x) = (3 + 0.50x)(38 - 4x), where x is the number of 50 cent price increases.

Step-by-step explanation:

The student is asking to complete an equation that models the relationship between the number of 50 cent price increases and the revenue generated in a book rental business. We start with the base revenue generation of $3 per book, renting out 38 books a day. Each 50 cent increase (represented as x) causes a drop in 4 rentals. The equation will have its slope and y-intercept adjusted based on these parameters.

Let's denote the base charge per book as $3 (when x=0), and the base number of books rented out as 38. Thus, the base revenue (y-intercept) is 3 * 38. For every 50 cent increase, the price per book increases by x * 0.50, but the number of books rented out reduces by 4x (because each increase reduces the number by 4). So, the revenue function, b(x), is given by:

b(x) = (3 + 0.50x)(38 - 4x)