Fitting a graph to data points.

[bon]

Homework Statement

I'm told that someone goes for a walk on some cliffs and given data for the total time of the trip and the distance traveled and the maximum height difference during the walk.

I'm asked to find a function for T(d,h) i.e. time taken as a function of distance and max height.

Data points:

Distance points (feet): 52800, 58080, 73920
Height points (corresponding to the above three - also in feet): 1500, 1300, 1000
Time points: (hours - again, corresponding): 5.4, 7.9, 6.7

Homework Equations

The Attempt at a Solution

I first assumed a simple proportionality like T = k dh and tried to find k but that didnt work..

what kind of proportionality should i be expecting?

Thanks

 

[Stephen Tashi]

You notation isn't clear. Guessing at what it means, maybe your are suppose to use
dT = k dh.

If that fails, you can always try T(h) = kh + c, where k and c are constants.
or h(T) = kT + c

 

[HallsofIvy]

Steven Tashi, bon specifically said that "d" is the distance walked, not a differential.

bon, since you are given three data points try something like T= ad+ bh+ c with three constants, a, b, and c. Putting in the data given gives you three equations to solve for a, b, and c.