Pregunta
A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of t app's price (in dollars) is modeled by \( P(x)=-2(x-3)(x-11) \) What would be the company's profit if the app price is 0 dollars? million dollars
Ask by Harmon Hammond. in the United States
Feb 22,2025
Solución de inteligencia artificial de Upstudy
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If the app price is 0 dollars, the company's profit is -66 million dollars.
Solución
We are given the profit function P(x) = -2(x - 3)(x - 11) (in millions of dollars) and need to determine the profit when the app price x is 0 dollars.
Step 1: Substitute x = 0 into the equation:
P(0) = -2(0 - 3)(0 - 11)
Step 2: Simplify the factors:
0 - 3 = -3
0 - 11 = -11
Step 3: Multiply the factors together:
(-3) × (-11) = 33
Step 4: Multiply by -2:
P(0) = -2 × 33 = -66
Thus, if the app price is 0 dollars, the company's profit would be -66 million dollars, indicating a loss of 66 million dollars.
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Simplifique esta solución Bonus Knowledge
To find the company's profit when the app price is 0 dollars, you can substitute \(x = 0\) into the profit function \(P(x)\): \[ P(0) = -2(0-3)(0-11) = -2(-3)(-11) = -2 \times 3 \times 11 = -66 \] Thus, the profit would be \(-66\) million dollars, indicating a substantial loss when the app is priced at no cost. If the app is offered for free, it can potentially attract a larger user base, potentially leading to future monetization strategies such as ads, in-app purchases, or premium features. However, it’s critical to consider costs, as losing money initially could impact the business's long-term sustainability.
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