How do I find the equation of a curve from a list of points on the curve?

Question

I used excel to create a line graph or curve that has pressure on the x-axis and volumetric storage capacity on the y-axis. My problem is that currently my x-axis ends at a value of (or pressure) of35 and I now need to use this curve to find storage capacities at pressures ranging from 160 to 510. How would I go about finding an equation that would allow me to insert a given pressure and have it give me the storage capacity volume?

My points on the curve are: (0,0); (3,25); (4.5,41.5); (6,46); (8,600; (11.5,75.5); (14.75,85.75); (18,91.25); (21.7,101); (25.5,109.25), (29,115.5); (32,121); (35,124)

Also I do have access to a TI-89 calculator, but am not sure how to use it to do this.

Answer 1

I would use Excel's built-in ability to create best-fit lines, complete with formulae. I plugged in your numbers and created a logarithmic trendline that was a pretty good fit. You can then use the function to predict storage capacity at higher pressures. You need to use the Chart Wizard to create an XY scatter plot, then right-click on any of the data points on the plot and select "Add Trendline."

Answer 2

Didn't your prof tell you that predicting that far outside the data range is meaningless-- but that's not what you asked.
Excel will find the equation for you.
Assuming you used X-Y (Scatter) to plot your chart-- Click on any data point on the chart so that all the points are highlighted. Click on Chart (top menu) > Add trendline > Highlight a choice that seems to fit > click on the Options tab > Check the two boxes at the left bottom (equation and R²) > OK
You should see the equation and the R² values on your chart. The R² will tell you how good your model is. It will be between 0 and 1--the higher, the better. Repeat the above steps with different models until you find the highest R².

Answer 3

In excel, you can use curve-fitting that will give you a function f(x). Then you can find f(160), f(510) etc..

Answer 4

enter your points into L1 and L2 under the STAT menu and perform different regressions (linear, quadratic, cubic, power, exponential, etc) and determine which seems to give the most accurate r^2 value.