A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 6 hours there will be 2400 bacteria. (a) Express the population P after t hours as a function of t. Be sure to keep at least 4 significant figures on the growth rate. P(t)= (b) What will be the population after 7 hours? bacteria (c) How long will it take for the population to reach 1010? Give your answer accurate to at least 2 decimal places. hours

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A: Please see the below picture for detailed solution.

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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.