A colony of bacteria is grown under ideal conditions in a laboratory so that the rate of increase of the bacteria population is proportional to the number of bacteria present. (a) Write down the differential equation that models this situation. (Define all the symbols that you use.) (b) Find the general solution of the differential equation in (a). (c) Solve this differential equation, given that at the end of 3 hours there are 10 000 bacteria and at the end of 5 hours there are 40 000.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.