Word problem on rates of change

[sully039]

Q) A crystal in the shape of a cube is growing in a test tube. Estimate the rate at which the surface area is changing with respect to the side length when the side length of the crystal is 3cm.

This question is from a lesson based on instantaneous rates, rate of change, etc. I don't really understand what to do since I'm kinda new to this unit. Could someone expain the steps on how to solve it so i can solve similar questions on my own?
*answer is 36cm^2/cm

Any help is appreciated.

[stapel_eliz]

Q) A crystal in the shape of a cube is growing in a test tube. Estimate the rate at which the surface area is changing with respect to the side length when the side length of the crystal is 3cm.

This question is from a lesson based on instantaneous rates, rate of change, etc.

The term "instantaneous rate" usually refers to derivatives, which is a technique you'll learn once you reach calculus. What method(s) are you supposed to use in algebra for finding instantaneous rates?

Thank you!

[sully039]

Well so far, I've learned to find instantaneous rates of change by setting up a table with intervals of numbers that approach x in (x,y). Using these intervals I'd then substitute the numbers into the model's equation and find change in f(x)/change in x.

But for this problem they do not give me an equation, so I'm How are you supposed to figure it out?

[stapel_eliz]

...for this problem they do not give me an equation, so I'm How are you supposed to figure it out?

By making your own equation!

A crystal in the shape of a cube is growing in a test tube. Estimate the rate at which the surface area is changing with respect to the side length when the side length of the crystal is 3cm.

What is the formula for the surface area of a cube with side-length "s"? Start from there.

[sully039]

Oh, so the formula would be 6s².

I ended up getting the right answer, thanks for the help.