M unfamiliar words for an upcoming test. The rate at which the student learns is proportional to the number of items remaining to be learned, with…

Mkytt(a) Write down the right hand side of the differential equation satisfied by y. (Your answer should be given in terms of y.)

dy

dt

= k(M−y)

(b) What is the initial value of y? (Give an exact answer.)

y(0) =

(c) Suppose that there are 140 words to be learned and that k = 0.7 per hour for this student. Recall that the solution to y’ = k(M − y)

with y(0) = 0

is given by y(t) = M(1 − e−kt).

(Give your answers correct to at least three decimal places.)How many hours would it take the student to learn the first 18 percent of the words?

hours

How long would it take to learn the next 18 percent of the words?

hours

How long would it take to learn the next 18 percent of the words?

hours

(d) The student has just finished learning the first 18 percent of the words. (Give your answers correct to at least three decimal places.)How long would it take to learn 18 percent of the

remaining

words?

hours

After doing this, how long would it take to learn 18 percent of the words that then remain?

hours