Assuming that the growth rate is the function of not only size but also time, the system of growth is reduced to
(dy)/(dt) = f(t,y)
where f(t,y) is the function of time t and size y. Let us assume that
f(t,y) = Cmt^^^<m-1>(A-y)
where A, C, and m are constants, a new growth equation
y = A(1-exp[-Ct^m])
is derived. This equation is the same as one which is created by adding an expanding factor to the Weibull distribution function.
To examine the applicablilty of this equation, the Weibull-type growth equation was applied to the observed growth of diameter, height, basal area, and volume of 52 trees. The Weibull type growth equation showed a good fit to the growth not only with a clear inflection but also without one, as compared with the Mitscherlich, the Logistic, and the Gompertz. It was recognized that many monotonically increasing growth phenomena could be modelled by this equation with various numerical values for the scale(C), the shape(m), and the upper asymptote(A) parameters.