Question

A popular video game retailer develops apps. The total profit, in dollars per day, after x days can be modeled by the function R(x) = 3x3 – 21x2 + 21x + 45. The total cost, in dollars per day, after x days, can be modeled by the function A(x) = x2 – 2x – 3. After how many days does the retailer start making money?

Answer 1

The retailer starts making money after approximately 2 days.

Step-by-step explanation:

To determine when the retailer starts making money, we need to find the point where the profit function, R(x), is greater than the cost function, A(x). Let's set up the inequality 3x^3 - 21x^2 + 21x + 45 > x^2 - 2x - 3.

Simplifying the inequality, we have 3x^3 - 21x^2 + 21x + 45 - x^2 + 2x + 3 > 0.

Combining like terms, we get 3x^3 - 22x^2 + 23x + 48 > 0.

The inequality can be solved graphically or by using a sign chart. After solving this, we find that the retailer starts making money after approximately 2 days.