Question

George has opened a new store and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x^2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.

He has also found that his expenses each month can be modeled by c(x)=x^2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.



What does (r−c)(3) mean about George's new store?


A)The new store will sell 3400 items in its third month in business.

​​B)The new store will have a profit of $2400 after its third month in business.

C)The new store will have a profit of $3400 after its third month in business.

​D)The new store will sell 2400 items in its third month in business.

Answer 1

(r-c)(3) means that you will simply plug in the value 3 as x in the functions r(x) and c(x) and take the difference of both.

Solving for the value of the functions we'll get:

`r(3)= (3)^(2)+5(3)+14=9+15+14=38`

`c(3)= (3)^(2)-3(3)+14=9-9+4=4`

`(r-c)(3)=38-4=34`

Since the value is positive, we can say that the store will profit in its third month. Knowing that r(x) and c(x) is measured in hundreds of dollars, we can also say that the profit will be $3400.

ANSWER: C. The new store will have a profit of $3400 after its third month in business.

Answer 2

Both r(x) and c(x) are in hundreds of dollars. The difference r(x) -c(x) is the excess of revenue over cost, hence profit. (r -c)(3) is the profit in hundreds of dollars when the store has been open 3 months. (r -c)(3) = 34, so the model says the store has a profit of 3400 dollars after being open 3 months.

Selection C is appropriate.