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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

$$20 = 200\left(1-e^{-k5}\right)$$

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up vote 2 down vote accepted

Just continue $$20=200(1-e^{-5k})$$ $$0.9=e^{-5k}$$ $$\ln0.9={-5k}$$

To solve (B), (C) and (D) just substitute the appropriate variable to solve for the others.

For instance, B) Insert t=10 with above k and solve for L(t)

C) Same as above with t=15

D) Put L(t) = 180 and solve for t.

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Thank you! The logarithms are really throwing me off right now... – Tyler Zika Nov 28 '12 at 23:53

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