Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). 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 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.

b(x) = -x2 + x +

b(x) = -2x² + 7x + 114

Step-by-step explanation:

Step-by-step explanation:

First we convert 50 cent into dollar,

1 cent = dollar

1 cent = 0.01 dollar

50 cent = 0.5 dollar

According to question,

x is the number of 50¢=$0.5 price increases.

b(x) is the revenue generated

He currently charges $3 per book.

i.e. price of book = 3+0.5x

Quantity or average = 38 per day

According to a study, for every 50¢ increase in rental price, the average business can expect to lose 4 rentals a day.

i.e. quantity became 38-4x

Revenue = Price × Quantity

The required equation is given by,

40 x 50 = 2000

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: