Select the correct answer. Mr. Walter is remodeling his house and wants to design a rectangular garden in the backyard. The width of the garden, \( W(A) \), in feet, is modeled by this equation, where \( A \) is the area of the garden, in square feet. \( W(A)=\sqrt{A}-1.24 \) What is the average rate of change of the garden's width when the garden's area changes from 289 square feet to 400 square feet? A. The garden's width increases by approximately 0.027 foot for every 1 -square-foot increase in the garden's area. B. The garden's width increases by approximately 0.27 foot for every 1 -square-foot increase in the garden's area. D. The garden's width increases by approximately 15.76 feet for every 1 -square-foot increase in the garden's area. D. The garden's width increases by approximately 18.76 feet for every 1 -square-foot increase in the garden's area. Next

To find the average rate of change of the garden's width \( W(A) \) as the area changes from 289 square feet to 400 square feet, we first calculate \( W(289) \) and \( W(400) \): For \( A = 289 \): \[ W(289) = \sqrt{289} - 1.24 = 17 - 1.24 = 15.76 \] For \( A = 400 \): \[ W(400) = \sqrt{400} - 1.24 = 20 - 1.24 = 18.76 \] Now, calculate the average rate of change: \[ \text{Average rate of change} = \frac{W(400) - W(289)}{400 - 289} = \frac{18.76 - 15.76}{111} = \frac{3}{111} \approx 0.027 \] So, the correct answer is A. The garden's width increases by approximately 0.027 foot for every 1-square-foot increase in the garden's area. Have you ever noticed how gardens can transform a space? With a rectangular layout, Mr. Walter's garden could become a serene haven filled with vibrant flowers or fresh vegetables! Plus, knowing how width and area relate can help in maximizing that outdoor space. When diving into garden design, consider not just dimensions but also sunlight, water access, and soil type. Many first-time gardeners miscalculate their planting layout or plant too closely together. Remember to leave ample space between plants for growth!