Population of Bacteria

The number of bacteria per cubic centimeter of culture increases under proper conditions at a rate proportional to the number present.  Find an expression for the number present at the end of time t.  Find the time required for the number per cubic centimeter to increase from b_{1} to b_{2}.  Does this time depend on the number present at the time t=0?

Source: March, Herman W., and Wolff, Henry C. (1917). Calculus. New York: McGraw-Hill. (Question 3, p. 158)

 

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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