The metabolic rate of a person who has just eaten a meal tends to go up and​ then, after some time has​ passed, returns to a resting metabolic rate. This phenomenon is known as the thermic effect of food. Suppose that for one particular​ person, the thermic effect of food is given by the following​ equation, where​ F ( t ) is the thermic effect of food​ ( in kJ / hr ) and t is the number of hours that have elapsed since eating a meal.  F ( t ) = - 10.35 + 175.8t e - t / 1.3 , for t > 0  a. Find F ' ( t ) . b. determine where the function F ( t ) is increasing and where it is decreasing. Interpret the answer.  Upon eating a meal, does this person's metabolic rate begin to increase, or does it begin to decrease? After how many 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.