5. A culture initially has 10000 bacteria. At t = 2h, there are 15000 bacteria. If the rate of growth is proportional to the number of bacteria P(t), present at time t, how long will it take for the population to reach 50000 bacteria? You must set up and solve an IVP for this problem. Don't start with P(t), rather set up an IVP and then find P(t).

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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.