i need to approximate profit in this equation
3. Hot Rocks Music sells CDs. If the profit can be approximated by following equation:
, where x represents the number of thousands of CDs sold.
Approximately, how many CDs must be sold in order for the company to make a profit?
To approximate the number of CDs that need to be sold in order for the company to make a profit, we can use the given equation and solve for x.
The equation represents the profit in terms of the number of thousands of CDs sold. Let's write the equation in a more mathematical form:
Profit = -0.1x^2 + 4x
We want to find the approximate value of x when the profit is greater than zero (indicating a profit). In other words, we need to solve the equation:
-0.1x^2 + 4x > 0
To solve this inequality, we can factor out x:
x(-0.1x + 4) > 0
Now, we need to find the values of x that satisfy this inequality. There are two cases:
1. When x > 0 and -0.1x + 4 > 0:
-0.1x + 4 > 0
-0.1x > -4
x < 40
2. When x < 0 and -0.1x + 4 < 0:
-0.1x + 4 < 0
-0.1x < -4
x > 40
Combining both cases, we find that x can be any value between -∞ and 0, or between 40 and +∞.
Therefore, to make a profit, the company must sell approximately more than 40,000 CDs.