Setting up equations that Define functions - word problem

[Rsls79]

Can anyone help me with this one? There are 2 parts to this question and I figured out the first but stuck on the next.

These questions are based off of this word problem that I figured out:

The perimeter of a rectangle is 100cm. Express the area of the rectangle in terns of the width.
Answer: 2x + 2L = 100
x + L = 50
L = 50 -x

Area = xL
= x(50 - x)
A(x)= 50x - x^2

The next parts I'm stuck on.

(2) The width x is increasing at the rate of 3 cm/min, and at time t = 0, the width x is 2 cm. Express the area of the rectangle as a function of time t.

During the time intervral from t=0 to t=16, when is the area of the rectangle increasing, decreasing?

Any help is much appreciated.


:?:

 

[Gene]

Chain rule.
dA/dt = dA/dx*dx/dt
dx/dt=3
x=2+3t

 

[Rsls79]

If you could, can you tell me why you used the chain rule. And is there another way to solve this without the chain rule because I don't quite get that rule yet.

 

[Gene]

It is an extremely handy tool. It is the first thing that leaps to mind when you want to change the dependent variable. In this case you can get the same effect by substituting
x=2-3t in the area equation.
A(t)= 50x-x^2 = 50(2-3t)-(2-3t)^2