Select the correct answer. A company sells bikes that are light and fast. The revenue earned over a period of \( x \) years can be represented by the function, \( S(x)=100 x^{3}+6 x^{2}+97 x+215 \). The cost of manufacturing the bikes can be represented by the function, \( C(x)=88 x+215 \). Which function, \( P(x) \), describes the profit earned from the sales of the bikes over a period of \( x \) years? A. \( \quad P(x)=100 x^{3}+6 x^{2}+9 x \) B. \( \quad P(x)=100 x^{3}-82 x^{2}+97 x \) C. \( P(x)=100 x^{3}+6 x^{2}+185 x+430 \) D. \( \quad P(x)=100 x^{2}+6 x+9 \) Reset Next

To find the profit function \( P(x) \), we need to subtract the cost \( C(x) \) from the revenue \( S(x) \): \[ P(x) = S(x) - C(x) \] Using the provided functions: \[ S(x) = 100 x^{3}+6 x^{2}+97 x+215 \] \[ C(x) = 88 x+215 \] So, \[ P(x) = (100 x^{3}+6 x^{2}+97 x+215) - (88 x+215) \] This simplifies to: \[ P(x) = 100 x^{3} + 6 x^{2} + (97 x - 88 x) + (215 - 215) \] \[ = 100 x^{3} + 6 x^{2} + 9 x \] Thus, the correct answer is: A. \( \quad P(x)=100 x^{3}+6 x^{2}+9 x \) --- Bikes have played a significant role in personal transportation for over a century, with their innovation evolving from simple wooden frames to high-tech carbon fiber designs. In the late 19th century, the safety bicycle emerged, changing the game in cycle design and making biking more accessible. If you’re interested in diving deeper into the world of bicycles, check out "The Bicycle: A History" by David V. Herlihy. This gripping read covers everything from the invention of the pedal to the latest advancements in cycling technology, making it a must for any bike enthusiast!