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 . Find the time required for the number per cubic centimeter to increase from to . Does this time depend on the number present at the time ?
Source: March, Herman W., and Wolff, Henry C. (1917). Calculus. New York: McGraw-Hill. (Question 3, p. 158)