The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. (a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.)  % (b) What was the initial size of the culture? (Round your answer to the nearest whole number.)  bacteria (c) Find a function that models the number of bacteria n(t) after t hours. (Enter your answer in the form  n0ert.  Round your  n0  value to the nearest whole number. Round your r value to two decimal places.) n(t) =  (d) Find the number of bacteria after 4.5 hours. (Round your answer to the nearest hundred.)  bacteria

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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.