The management at a plastics factory has found that the maximum number of units a worker can produce in a day is 45. The learning curve for the number N of units produced per day after a new employee has worked t days is modeled by  N = 45(1 − ekt).  After 20 days on the job, a new employee produces 18 units. (a) Find the learning curve for this employee. (Hint: First, find the value of k. Round your value of k to three decimal places.)   (b) How many days does the model predict will pass before this employee is producing 27 units per day? (Round your answer to the nearest whole number.)

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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.