Question

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The initial surface area of a puddle on a concrete playground is 123 ft². The rate of change of the surface area with respect to time (in minutes) is directly proportional to the surface area A(t). After 5 minutes, the surface area is 105 ft²

a) Write the DE to be solved to find the equation for A(t)

b) Solve the equation in a), subject to the boundary value condition.

c) After how many minutes will the surface area be 50 ft²?

Answer 1

a)

So that is the differential equation

b) and

means

Therefore,

Which means

Initial conditions imply

So

And so

That is, is the required general solution

c) minutes

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