Psychologists sometimes use the function
$L(t) = A\left(1 - e^{-kt}\right)$
to measure the amount $L$ learned at time $t$. The number $A$ represents the amount to be learned, and the $k$ measures the rate of learning. Suppose that the student has an amount $A$ of $200$ words to learn. A psychologist determines that the student learned $20$ words after $5$ minutes.
(A) Determine the rate learning of $k$.
(B) Approximately how many words will student have learned after $10$ minutes?
(C) After $15$ minutes?
(D) How long does it take for the student to learn $180$ words?
Sorry guys but I'm completely lost on how to approach this. I know the starting equation is
$L(t) = A\left(1-e^{-kt}\right)\;.$
Then with info put into the equation
$20 = 200\left(1-e^{-k5}\right)$