Exponential Growth and Decay

Abstract

The values of A and k for the exponential

$$x = A{e^{ - kt}}$$

((24.1))

are determined from the n data points (t _i , X _i ) by plotting the natural logarithm of X _i against t _i . The resulting plot is linear with slope — k and intercept ln A. Linear regression (Procedure 3) is used on the pairs (t _i , ln x _i ). The value of k is related to the half-life t_1/2 as k = ln 2/t_1/2 ≈ 0.693/t_1/2.