The annual yield per lemon tree is fairly constant at 350 pounds per tree when the number of trees per acre is 150 or fewer For each additional tree over 150 , the annual yield per tree for all trees on the acre decreases by 8 pounds due to overcrowding. a. Express the yield per tree, Y , in pounds, as a function of the number of lemon trees per acre, x , where x is greater than 150 . b. Express the total yield for an acre, \( T \), in pounds, as a function of the number of lemon trees per acre, x , where x is greater than 150 a. \( Y(\mathrm{x})=\square \)

To find the yield per tree \( Y(x) \) for lemon trees when the number of trees per acre \( x \) is greater than 150, we start with the base yield of 350 pounds at 150 trees. For each tree beyond 150, the yield decreases by 8 pounds. Hence: \( Y(x) = 350 - 8(x - 150) \) This simplifies to: \( Y(x) = 350 - 8x + 1200 \) So: \( Y(x) = 1550 - 8x \) Next, to express the total yield \( T(x) \) in pounds for an acre, we multiply the yield per tree \( Y(x) \) by the number of trees \( x \): \( T(x) = x \cdot Y(x) = x(1550 - 8x) \) Thus, we have: \( T(x) = 1550x - 8x^2 \) So, to summarize: a. \( Y(x) = 1550 - 8x \) b. \( T(x) = 1550x - 8x^2 \) Did you know that lemon trees can live for over 50 years and keep producing fruit! It's fascinating how such a resilient tree has a direct impact on agriculture, economics, and even culinary practices around the globe. The versatile lemon is not just a tangy delight but also a staple in many cultures! If you enjoy delving deeper into botany and agriculture, you might want to explore books on permaculture or organic farming. They often include insights on maximizing yields sustainably, alongside other plants and crops! Happy reading!