# Which formula will calculate values shown in this graph?

First, sorry about a n00b question.

Here's the graph:

The x=30, y=0.5 is an approximation. The other two dots are measured. My goal is to mathematically describe/calculate y based on arbitrary x value.

Context

I'm regulating heating with Raspberry Pi and I have noticed that, to get increase of 1 deg C, the heating needs to work for 1/2 hours when the outside-inside temperature difference is ~10 deg. C. The measured time needed to increase room temp for 1 deg C rises to 1 hour when the in-out diff is 20 deg C. (And, as I said, 30 deg delta is approximated, for now).

The heating_speed (y axis, measured in C/h) as function of temp_delta (x axis, measured in C) just "feels" that it can not be linear. But, I could be mistaken.

Additionally, I'm not interrested in the freaky border cases when the in-out temp delta is > 40 C. In those cases, I believe, the current heating power will not be sufficient to keep the temperature stabile and it will probably have negative heating_speed.

Alternate assumption

Possibly, the function is linear, like this (blue):

In this case, I guess, the formula will be this: 3.-0.1 x. WA link 1, link 2.

• There is an infinite number of functions which could go through your two points. You must decide first on the type of formula you want to use, then compute its parameters and then extrapolate or interpolate for any arbirary value of x. Nov 27 '13 at 10:36
• @Saran Please provide some context so we can better help you. How did you encounter this? Nov 27 '13 at 10:37
• @GitGud I've added some "context". Nov 27 '13 at 11:17
• Here's a WA link. Nov 27 '13 at 11:27
• If you would plot instead $y = \mbox{temp_delta}$ and $x = \mbox{h} = t =$ heating time, then doesn't the graph become an exponential function, like $exp(-t/\tau)$ with $\tau$ a decay time ? Such exponentials are rather common with heating problems, in my experience. Moreover, a few measurements would then enable you to determine the function. In general, it's advisable to develop a mathematical model (with some free parameters) of the phenomenon, instead of trying to adapt to a ("randomly chosen") curve. Nov 27 '13 at 12:06

• The curve could also be like $1-exp(-t/\tau)$ ; can't get a clear picture from the available information. Nov 27 '13 at 12:12