Question

A company models its revenue in dollars using the function P(x)=70,000(x−x4) on the domain (0, 1) where x is the price at which they sell their product in dollars. Use a graphing calculator to sketch a graph and find the price at which their product should be sold to make revenue of $20,000. List the possible prices from least to greatest.

Answer 1

The x-coordinate of the intersection point will give you the price at which the revenue is $20,000.

To find the price at which the company's product should be sold to make a revenue of $20,000, we can use the given function P(x) = 70,000(x - x^4) on the domain (0, 1), where x is the price at which they sell their product in dollars.

To find the price at which the revenue is $20,000, we need to set the revenue function P(x) equal to $20,000 and solve for x:

`\[ P(x) = 70,000(x - x^4) = 20,000 \]`

To solve this equation, we can rearrange it:

`\[ x - x^4 = (20,000)/(70,000) \]`

`\[ x - x^4 = (2)/(7) \]`

Now, we can use a graphing calculator to sketch the graph of
`\( P(x) = 70,000(x - x^4) \)` and find the intersection point where P(x) is equal to $20,000.

Here's a general guide for using a graphing calculator:

1. Enter the function:
`\( P(x) = 70,000(x - x^4) \).`

2. Enter the horizontal line
`\( y = 20,000 \).`

3. Find the intersection point

The x-coordinate of the intersection point will give you the price at which the revenue is $20,000.