Answer:
(r - c)(4) means "The new store will have a profit of $4500 after its fourth month in business" ⇒ 3rd answer
Step-by-step explanation:
George has opened a new store and he is monitoring its success closely
He has found that:
- 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
- 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
∵ r(x) = x² + 6x + 10
∵ r(x) is the revenue
∵ c(x) = x² - 4x + 5
∵ c(x) is the expenses
- The profit is the difference between the revenue and the
expenses
∴ The profit = r(x) - c(x)
∵ r(x) - c(x) can me written as (r - c)(x)
∴ The profit = (r - c)(x)
∴ The profit = (x² + 6x + 10) - (x² - 4x + 5)
- Remember (-)(-) = (+) and (-)(+) = (-)
∴ The profit = x² + 6x + 10 - x² + 4x - 5
- Add the like terms
∴ The profit = (x² - x²) + (6x + 4x) + (10 - 5)
∴ The profit = 10x + 5
∴ (r - c)(x) = 10x + 5
- Substitute x by 4
∵ x = 4 ⇒ 4 months
∴ (r - c)(4) = 10(4) + 5
∴ (r - c)(4) = 45
∵ r and c are in hundred dollars
∴ The profit = $4500
(r - c)(4) means "The new store will have a profit of $4500 after its fourth month in business"
