A biologist is researching a newly discovered species of bacteria. At time t = 0, he puts 200 bacteria into what he has determined to be a favorable growth . Eight hours later , he measures 800 bacteria. This can be modeled by the equation , where a is the initial amount of bacteria. a. Find the rate of growth, k, of the bacteria, then determine the equation that models this situation.  b. How many bacteria are present at time t = 14? c. At what time will the number of bacteria reach 10,000?

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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.