Psychologists sometimes use the function L(t) = A(1 - e-kt ) to measure the amount L learned at time t. Here A represents the amount to be learned, and the number k measures the rate of learning. Suppose that a student has an amount A of 200 vocabulary words to learn. A psychologist determines that the student has learned 20 vocabularywords after 5 minutes.(a) Determine the rate of learning k.(b) Approximately how many words will the student have learned after 10 minutes?(c) After 15 minutes?(d) How long does it take for the student to learn 180 words?

Q: evaluate the function for each value.

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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.