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+6x+10 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)(4) mean about George's new store?

Answer 1

The new store will have a profit of $4500 after its fourth month in business.

Explanation:

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Answer 2

(r - c)(4), is the profit made in George's new store after 4 months which is $4,500

Explanation:

The given parameters for George's store are;

The amount of revenue George makes each month, r(x) = x² + 6·x + 10

The expenses each month, c(x) = x² - 4·x + 5

Where;

x = The number of months the store has opened the doors

r(x) and c(x) are measured in hundreds of dollars

The amount of profit from the store, P = Revenue - Expenses

Therefore, the profit made on a given month, x, is P(x), which is found as follows;

P(x) = r(x) - c(x) = (r - c)(x)

Therefore, (r - c)(4) = P(4), is the profit realized from George's new store, after 4 months

(r - c)(4) = 4² + 6·4 + 10 - (4² - 4·4 + 5) = 45