A bacteria culture grows with a constant relative growth rate. After 2 hours there are 600 bacteria and after 8 hours the count is 75,000. (a) Find the initial population.P(0) =  bacteria(b) Find an expression for the population after t hours.P(t) =        (c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.)P(7) =  bacteria(d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.)P'(7) =  bacteria/hour(e) When will the population reach 200,000? (Round your answer to one decimal place.)t =  hours

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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.