Question: Psychologists sometimes use the function L(t) = A(1 e -kt ) to measure the amount L learned at time t. The number A represents

Psychologists sometimes use the function

L(t) = A(1 – e^-kt)

to measure the amount L learned at time t. The number 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 learned 20 vocabulary words after 5 minutes.

(a) Determine the rate of learning k.

(b) Approximately how many words will the student have learned after 10 minutes?

(d) How long does it take for the student to learn 180 words?

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