Differential Equation (Application)

A population of mice, initially numbering 30, is kept in conditions that can support a population size of 120.  The rate of increase in the population of size N is assumed to be given by the equation \displaystyle \frac{dN}{dt}=cN\left(K-N\right), where c and K are positive constants.  Find the formula giving the number of mice t months later, if, after one month, the population numbers 80.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 5, p. 132)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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