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?

40
20
10
5

Answer 1

Answer:

The answer is 5.

Step-by-step explanation:

I took the quiz but this is how I did it:

You go into desmos, put in  R(x) divided by A(x) as the graph formula, and then boom!

Answer 2

The retailer starts making profit after 5 days.

Revenue is the total money gotten from selling a number of goods. Cost is the total amount of money spent to produce a number of goods.

Profit is the difference between revenue and cost. It is given by:

Profit = revenue - cost

Given that:

Revenue R(x) = 3x³ – 21x² + 21x + 45, Cost A(x) = x² – 2x – 3.

Therefore:

Profit = revenue - cost

Profit = 3x³ – 21x² + 21x + 45 - (x² – 2x – 3)

Profit = 3x³ – 22x² + 23x + 48

To make profit, Profit > 0, hence:

3x³ – 22x² + 23x + 48 > 0

Solving gives: x = -1 or 3 or 5.3

Therefore the retailer starts making profit after 5 days.

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