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The area A(r)(in square meters) of a circular algae colony with radius r meters is given by A(r)=pir^2. Basically that's A(r)= pi r square.The radius M(t)(in meters) after t minutes is given by M(t)= 10/3 t.Write a formula for the areaZ(t)(in square meters) of the algae colony colony after t minutes.You don't have to simplify. Thanks.

Respuesta :

aramisdegaula1977

Answer:

The expression provided by the area (square meters) is given by:  [tex]A(t) = pi \frac{100t^{2} }{9}[/tex].

Step-by-step explanation:

The area of the algae colony is a function of the radius r (meters), so [tex]A(r) = \pi r ^ 2[/tex].

The radius of the circle formed by the algae colony is a function of time t (in minutes), so [tex]M (t) = \frac{10t }{3}[/tex]. So,

[tex]A(r) = \pi r ^ 2[/tex]  [Substituting the expression for radius]

[tex]A(t) = pi (\frac{10t }{3})^{2} = pi \frac{100t^{2} }{9}[/tex]

Then the expression provided by the area (square meters) is given by:  [tex]A(t) = pi \frac{100t^{2} }{9}[/tex].