A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the bacteria is untreated, the rate of growth of the population is directly proportional to the size of the population, dPdt=ktdPdt=kt. The general solution to this differential equation is P=CektP=Cekt, where P is the current size of the population and t is the number of days since measurement began.   If untreated, how long until the population of the bacteria colony reaches 100,000? (Use 3 decimal places)

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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.