QuestionAugust 18, 2025

Select the correct answer. An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed.company as p(x)=x^3-4x^2+5x-20 where p is in hundreds of dollars and x is number of years the company has been in business. In which year (x) will the entrepreneur break even? A. year 1 B. year 2 C. year 3 D. year 4

Select the correct answer. An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed.company as p(x)=x^3-4x^2+5x-20 where p is in hundreds of dollars and x is number of years the company has been in business. In which year (x) will the entrepreneur break even? A. year 1 B. year 2 C. year 3 D. year 4
Select the correct answer. An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed.company as p(x)=x^3-4x^2+5x-20 where p is in hundreds of dollars and x is number of years the company has been in business. In which year (x) will the entrepreneur break even? A. year 1 B. year 2 C. year 3 D. year 4

Solution
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Answer

D. year 4 Explanation 1. Set the profit equation to zero To find when the entrepreneur breaks even, set p(x) = 0: x^3 - 4x^2 + 5x - 20 = 0. 2. Test integer values for x Substitute integer values for x to find when p(x) = 0. - For x = 1: 1^3 - 4(1)^2 + 5(1) - 20 = 1 - 4 + 5 - 20 = -18 \neq 0 - For x = 2: 2^3 - 4(2)^2 + 5(2) - 20 = 8 - 16 + 10 - 20 = -18 \neq 0 - For x = 3: 3^3 - 4(3)^2 + 5(3) - 20 = 27 - 36 + 15 - 20 = -14 \neq 0 - For x = 4: 4^3 - 4(4)^2 + 5(4) - 20 = 64 - 64 + 20 - 20 = 0 3. Verify solution The calculation shows p(4) = 0, confirming break-even at year 4.

Explanation

1. Set the profit equation to zero<br /> To find when the entrepreneur breaks even, set $p(x) = 0$: $x^3 - 4x^2 + 5x - 20 = 0$.<br />2. Test integer values for x<br /> Substitute integer values for $x$ to find when $p(x) = 0$. <br />- For $x = 1$: $1^3 - 4(1)^2 + 5(1) - 20 = 1 - 4 + 5 - 20 = -18 \neq 0$<br />- For $x = 2$: $2^3 - 4(2)^2 + 5(2) - 20 = 8 - 16 + 10 - 20 = -18 \neq 0$<br />- For $x = 3$: $3^3 - 4(3)^2 + 5(3) - 20 = 27 - 36 + 15 - 20 = -14 \neq 0$<br />- For $x = 4$: $4^3 - 4(4)^2 + 5(4) - 20 = 64 - 64 + 20 - 20 = 0$<br /><br />3. Verify solution<br /> The calculation shows $p(4) = 0$, confirming break-even at year 4.
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