The size P of a certain insect population at time t​ (in days) obeys the function P(t)=500e0.02t. ​(a) Determine the number of insects at t=0 days. ​(b) What is the growth rate of the insect​ population? ​(c​) Graph the function using a graphing utility. ​(d) What is the population after 10​ days? ​(e) When will the insect population reach 750​? ​(f) When will the insect population​ double?     ​(a) The number of insects at t=0 days is_____ insect(s).

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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.