select the correct answer. mr. walter is remodeling his house and wants to design a rectangular garden in…

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)=√a - 1.24 what is the average rate of change of the gardens width when the gardens area changes from 289 square feet to 400 square feet? a. the gardens width increases by approximately 15.76 feet for every 1 - square - foot increase in the gardens area. b. the gardens width increases by approximately 0.27 foot for every 1 - square - foot increase in the gardens area. c. the gardens width increases by approximately 0.027 foot for every 1 - square - foot increase in the gardens area. d. the gardens width increases by approximately 18.76 feet for every 1 - square - foot increase in the gardens area.

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)=√a - 1.24 what is the average rate of change of the gardens width when the gardens area changes from 289 square feet to 400 square feet? a. the gardens width increases by approximately 15.76 feet for every 1 - square - foot increase in the gardens area. b. the gardens width increases by approximately 0.27 foot for every 1 - square - foot increase in the gardens area. c. the gardens width increases by approximately 0.027 foot for every 1 - square - foot increase in the gardens area. d. the gardens width increases by approximately 18.76 feet for every 1 - square - foot increase in the gardens area.

Answer

Explanation:

Step1: Calculate width at $A = 289$

Substitute $A = 289$ into $W(A)=\sqrt{A}-1.24$. $W(289)=\sqrt{289}-1.24=17 - 1.24 = 15.76$

Step2: Calculate width at $A = 400$

Substitute $A = 400$ into $W(A)=\sqrt{A}-1.24$. $W(400)=\sqrt{400}-1.24=20 - 1.24 = 18.76$

Step3: Calculate average rate of change

The average rate of change formula is $\frac{W(400)-W(289)}{400 - 289}$. $\frac{18.76 - 15.76}{400 - 289}=\frac{3}{111}\approx0.027$

Answer:

C. The garden's width increases by approximately 0.027 foot for every 1 - square - foot increase in the garden's area.