# Working out an equation

1. Nov 27, 2009

### nobahar

Hello!
Theres a relationship in which the temperature decreases with time:
It starts at 100 degrees C, then decreases by 10, then 9, then 8, then 7 and so on per minute. Is it possible to come up with a function for this? I tried working back from the second derivitive, which is +1, then integrated it with respect to time:
$$\int{1} dx = x + c$$
I figured since it starts by removing 10 from 100, then c = -10.
I then took the integral of this:
$$\int{x - 10) dx = \frac{x^2}{2} - 10x + c$$
Can I get this to fit what I need? It goes wrong from here as I don't think this fits what I need.

2. Nov 27, 2009

### pbandjay

Just because it starts decreasing by ten, doesn't mean it always decreases by ten.

Integrating:
f''(x) = 1
f'(x) = x + c
f(x) = x2/2 + cx + d

And you have that f(0) = 100 and f(1) = 90, so use those to find c and d (or use any two initial conditions that you want).

I tested some values in the final equation that I got:

x - f(x)
0 - 100
1 - 90
2 - 81
3 - 73
4 - 66

3. Nov 27, 2009

### nobahar

Thanks pbandjay.