Questions: USE TOOLS A company models its revenue in dollars using the function P(x)=70,000(x-x^4), where x is the price at which they sell their product in dollars. Use a graphing calculator to find the price at which their product should be sold to make revenue of 20,000.

USE TOOLS A company models its revenue in dollars using the function P(x)=70,000(x-x^4), where x is the price at which they sell their product in dollars. Use a graphing calculator to find the price at which their product should be sold to make revenue of 20,000.
Transcript text: 15. USE TOOLS A company models its revenue in dollars using the function $P(x)=70,000\left(x-x^{4}\right)$, where $x$ is the price at which they sell their product in dollars. Use a graphing calculator to find the price at which their product should be sold to make revenue of $\$ 20,000$.
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Solution

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Solution Steps

Step 1: Define the Revenue Function

The revenue function is given by \( P(x) = 70,000(x - x^4) \). We need to find the price \( x \) such that the revenue equals \$20,000. Therefore, we set up the equation: \[ 70,000(x - x^4) = 20,000 \]

Step 2: Rearrange the Equation

Rearranging the equation gives us: \[ 70,000(x - x^4) - 20,000 = 0 \] This simplifies to: \[ 70,000x - 70,000x^4 - 20,000 = 0 \]

Step 3: Solve for \( x \)

To find the value of \( x \) that satisfies the equation, we can use numerical methods. The solution yields: \[ x \approx 0.29309378 \] This value represents the price at which the product should be sold to achieve a revenue of \$20,000.

Final Answer

\(\boxed{x \approx 0.2931}\)

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