Assume that a rectangle with sides x and y is expanding with time. Let y = 2x and x(t)=2t+5. What is the rate of change of the area when t=2?

Answer 1

The area A = x*y
We already know that y = 2x, so we can substitute that in:

A = x*2x = 2x^2

We were given that x(t) = 2t+5

A = 2x^2 = 2(2t +5)^2
A = 2(4t^2 + 10t + 25)
A(t) = 8t^2 + 20t + 25

The rate of change of the area with respect to time is dA/dt

dA/dt = 16t + 20

When t=2, dA/dt = 36