Chapter 4.4, Problem 128AYU

Learning Curve Psychologists sometimes use the function

$\text{L}\left(t\right)=\text{ A}\left(1-e^{-Kt}\right)$

to measure the amount $L$ learned at time $t$. Here $A$ represents the amount to he 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 $20$ vocabulary words after $5$ minutes.

Determine the rate of learning $k$.

Approximately how many words will the student have learned after $10$ minutes?

After $15$ minutes?

How long does it take for the student to learn $180$ words?