Supplementary Problems 1. A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria's population increased to 20,000. If the number of colonies grows exponentially, write a formula for the number of bacteria in the dish at any time t, where t is in hours. 2. In a farm, there initally were 10 rabbits. After three months, there are already 20 rabbits. Assuming that the growth is exponential and no rabbit dies in the process, at what time will there be 100 rabbits?

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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.