Math question in regards to functions in the form (1) / ( b ^ c )

I've found functions which follow the pattern of 1 / b^c produce nice curves which can be coupled with interpolation functions really nicely.

The way I use the function is by treating 'c' as the changing value, i.e. the interpolation value between 0 and 1, while varying b for 'sharpness'. I use it to work out an interpolation value between 0 and 1, so generelly the function I use is as such:

float interpolationvalue = 1 - 1/pow(100,c);
linearinterpolate( val1, val2, interpolationvalue);

Up to this point I've been using a hacked approach to make it 'work' since when interpolation value = 1 the value is very close to but not quite 0.

So I was wondering, is there a function in the form of or one which can reproduce similar curves to the ones produced by 1 / b^c where at c = 0 result = 1 and c = 1 result = 0.

Or even C = 0, result = 0 and C = 1 result = 1.

Thanks for any help!

For interpolation the approach offering the most flexibility is using splines, in your case quadratic splines would seem sufficient. The wikipedia page is math heavy, but you can find adapted desciptions on google.