How many words are memorized in the first 8 minutes?

Question

Suppose that in a memory experiment the rate of memorizing is given by , where  is the memory rate, in words per minute. How many words are memorized in the first 8 minutes?   wordsRound your answer to the nearest whole word

Answer 1

So we have the instantaneous rate of change, M'(t), but we want to know the number of words at t. The derivative suggests (correctly so) that we will need to take the integral of M'(t) to find the equation for M(t). We want the integral evaluated from t=0 to t=8.

∫-0.008t² + 0.2t

= -0.008/3t³+0.2/2t² evaluated from t=0 to t=8

= -0.00267t³+0.1t²

= (-0.00267(8)³+(0.1)8²)-0

= 1.365 + 6.4

= 7.765

We round to the nearest whole word which is 8.