Statistics Solutions

(See Solution) In a discussion of diffusion of a new process into a market, Hurter and Rubenstein refer to an equation of the from Y=k α^beta^t where

Question: In a discussion of diffusion of a new process into a market, Hurter and Rubenstein refer to an equation of the from

\[Y=k \alpha^{\beta^{t}}\]

where \(Y\) is the cumulative level of diffusion of the new process at time \(t\) and \(k, \alpha\) and \(\beta\) are positive constants. Verify their claim that

\[\frac{d Y}{d t}=k \alpha^{\beta^{t}}\left(\beta^{t} \ln \alpha\right) \ln \beta\]

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