I am working on an analysis that involves polygons and points with values and I am using IDW to predict the values of pixels in between. I need the values of the points to have a 50% impact on the values of the surrounding pixels when they are 3 miles away from the source data and a 0% impact when they are 5 miles away. I am wondering if anyone knows of a formula I could use to determine what power value would get me the results I am looking for. I'm basing this slightly off of a graph that is on one of the help pages for the IDW tool, a copy of which is attached. I'm hoping that there is a formula that would generate those different curves.

Is this possible or does anyone have any ideas?

Thanks

Is this possible or does anyone have any ideas?

Thanks

As for the weights, here's how it's done using the simple IDW formula of inverse-distance-squared weight and setting it to 0.5:

Here's a check in the Python window to make sure I got that right:

Remember these weights are *relative*: if two points are equal distance they both get 50% each weight, if only one point is in distance, it gets 100% weight.