How this calculation works
The factor b acts once per unit of x. For a two-unit interval, the ratio of the y-values is b².
THE FORMULA
b = exp[(ln y₂ − ln y₁)/(x₂ − x₁)], A = y₁/bˣ¹A worked example
(0,3) and (2,12) give y = 3 × 2ˣ.
Good to know
Use distinct x-values and positive y-values.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Fit y = A bˣ through two positive observations and report the growth factor.
The primary result is labeled “Growth factor per x unit”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use distinct x-values and positive y-values.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
(0,3) and (2,12) give y = 3 × 2ˣ.
Which rule does this calculator apply?
b = exp[(ln y₂ − ln y₁)/(x₂ − x₁)], A = y₁/bˣ¹