Question

For a given musical artist, the amount of profit is a quadratic model dependent upon the number of albums sold. If there are no albums sold, $7000 will be lost, and 40 albums will produce a profit of $13,000.

a. Write an equation expressing profit in terms of albums. Show your work.
b. Find the 'break-even' point.
c. How many albums must be sold to reach a profit of $20,000? Show your work.

Answer 1

To write an equation expressing profit in terms of albums, substitute the given values into the quadratic formula. The 'break-even' point is the number of albums where profit is zero. To find the number of albums for a profit of $20,000, set the profit equation equal to $20,000 and solve for x.

Step-by-step explanation:

a. To write an equation expressing profit in terms of albums, we can use the quadratic formula: ax^2 + bx + c = 0. Since we know that 40 albums produce a profit of $13,000 and no albums sold result in a loss of $7,000, we can substitute these values into the equation to solve for a, b, and c.

b. To find the 'break-even' point, we need to find the number of albums sold where the profit is zero. This can be done by setting the profit equation equal to zero and solving for x.

c. To find the number of albums that must be sold to reach a profit of $20,000, we can set the profit equation equal to $20,000 and solve for x.