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) = x² + 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) = x² - 4x + 5 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) (5) mean about George's new store?​

A. the new store will sell 5400 items in its fifth month in business
B. The new store will have a profit of $5400 after its fifth month in business
C. The new store will have a profit of $900 after its fifth month in business
D. The new store will sell 900 items In its fifth month in business

Answer 1

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54