In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If it is found that the number doubles in 6 hrs, how many may be expected at the end of 18 hrs? (b) If there are 10^2 at the end of 4 hrs, and 8x10^2 at the end of 8 hrs, how many were there in the beginning?

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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.