a business plan is centered around a circular area of distribution. the plan calls for the radius of the…

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)=\\(\\pi r^{2}\\); r in miles what is a(r(y)), the total area in y years? o a(r(y)) = 50\\(\\pi y^{2}\\) o a(r(y)) = 2,500\\(\\pi y^{2}\\) o a(r(y)) = 50\\(\\pi r^{2}\\) o a(r(y)) = 2,500\\(\\pi r^{2}\\)

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)=\\(\\pi r^{2}\\); r in miles what is a(r(y)), the total area in y years? o a(r(y)) = 50\\(\\pi y^{2}\\) o a(r(y)) = 2,500\\(\\pi y^{2}\\) o a(r(y)) = 50\\(\\pi r^{2}\\) o a(r(y)) = 2,500\\(\\pi r^{2}\\)

Answer

Explanation:

Step1: Sustituir la función de radio en la función de área

Dado que $r(y) = 50y$ y $A(r)=\pi r^{2}$, sustituimos $r$ por $r(y)$ en $A(r)$. $A(r(y))=\pi(50y)^{2}$

Step2: Simplificar la expresión

$(50y)^{2}=50^{2}y^{2}=2500y^{2}$, entonces $A(r(y))=\pi\times2500y^{2}=2500\pi y^{2}$

Answer:

$A(r(y)) = 2,500\pi y^{2}$