calc
posted by daryl on .
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?

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