DE problem, can it be that easy?

[somebodyelse5]

Homework Statement

Here is the problem. Is it as easy as my attempted solution? I think its more difficult but I am completely lost.

The Attempt at a Solution

simply integrate 1/.8S dS = 1 dt
use 2009 as start time so t=0 and S=.6 to solve for C

 

[Dick]

Sure, the price of sand has nothing to do with the price of glass so you are right. You can solve it that way. On the other hand it looks to me like the question isn't asking to you solve the equation. It's asking for an estimate of the solution using 'linearity principals'. That's different from solving. Are there more parts? They must have a question having something to do with glass later on, given the elaborate set up.

 

[somebodyelse5]

Sure, the price of sand has nothing to do with the price of glass so you are right. You can solve it that way. On the other hand it looks to me like the question isn't asking to you solve the equation. It's asking for an estimate of the solution using 'linearity principals'. That's different from solving. Are there more parts? They must have a question having something to do with glass later on, given the elaborate set up.

nope, that's it, I scanned everything involved. this is the last problem.

I would guess linearity, but we covered it for like 20 minutes and moved on. If I were to use linearity, where would I start?

 

[Dick]

You know dS/dt and S in 2009. The only linearity principal that comes to mind is to use that slope to extrapolate along a straight line to 2011. That gives you a pretty poor estimate of the actual solution you would get solving the ODE. And the reason why it's poor has nothing to do with the extraneous 'glass' stuff. It's just that the function isn't very closely approximated by a linear function. I really don't get what this question's point is. Maybe you should just solve the ODE and give that answer.