1. a. Show that the population P in the logistic equation reaches half the maximum pop- ulation M at time t* given by t* = to − (1/rM) In[Po/(M — Po)] g. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 11.1 Population Growth 469 b. Derive the form given by Equation (11.12) for population growth according to the logistic law. c. Derive the equation ln[P/(M – P)] = rMt – rMt* from Equation (11.12).

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