Exponential Function from Two Points Calculator
Find a and b in y=a·b^x from two positive data points, then evaluate the model at another x.
Formula
k=ln(y₂/y₁)/(x₂−x₁); b=e^k; a=y₁e^(−kx₁); y=a·b^x
Coefficient a ≈ exp(ln((2))-(0.6931471806)×(0)) · Base b ≈ exp((0.6931471806)) · Model value y ≈ exp(ln((2))+(0.6931471806)×((3)-(0)))
How to use
- Enter two points with distinct x and positive y.
- Enter the x at which to evaluate the model.
- Read a, b and the predicted y.
Examples
- Through (0,2) and (1,4): y=2·2^x, so y(3)=16.
Frequently asked questions
Must the x values differ?
Yes. Equal x values do not determine a unique model. Values too large or small to represent are rejected.
What if both y values are equal?
The tool returns the constant limiting case b=1.
Is this a regression forecast?
No. It passes through exactly two points. Extrapolation assumes the same multiplicative trend.
Sources
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