a business plan is centered around a circular...
a business plan is centered around a circular area of distribution. the plan calls for the radius of the distribution to increase 50 miles per year. the investors have asked that the plan include a reference to the area of distribution based on the number of years in business. these functions model this plan: radius in y years: r(y)=50y total area: a(r)=πr²; r in miles what is a(r(y)), the total area in y years? o a(r(y)) = 50πy² o a(r(y)) = 2,500πy² o a(r(y)) = 50πr² o a(r(y)) = 2,500πr²
Answer
# Answer:
A. $A(r(y)) = 2500\pi y^{2}$
# Explanation:
## Step1: Substitute $r(y)$ into $A(r)$
$A(r(y))=\pi(r(y))^{2}$
## Step2: Replace $r(y)$ with $50y$
$A(r(y))=\pi(50y)^{2}$
## Step3: Expand $(50y)^{2}$
$(50y)^{2}=50^{2}y^{2}=2500y^{2}$
So $A(r(y)) = 2500\pi y^{2}$