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exponential help


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this isn't really homework, just something i'm fiddling with.

let's say 100% of all people earn a dollar or more;

and 90% of all people earn 10 dollars or more;

and 50% of all people earn 20 dollars or more;

and 33% of all people earn 30 dollars or more;

and no one earns more than 40 dollars;

can you write an equation that goes though the other values? (can you compute say 2 dollars or more?)

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Yeah, it's a little vague.

I'm rusty on math, but I don't think there are any continuous and differentiable functions that are zero everywhere except for a specific region.

If it doesn't have to be differentiable, you could just construct a composite function with linear parts or maybe stitch together bezier curves.

If it doesn't have to be continuous except for the region between $1 and $40, you could just use something like f(x | a, b, c, d) = a*e^[-(x - b)^c / d] and solve for a, b, c, d.

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