Score: $26.5 / 30 \quad 23 / 25$ answered
Question 25
『0/1 pt $2 \rightleftarrows 96$ (i) Details
You are memorizing words for a vocabulary test. You studied a few days ago, and you know 23 word already. It is the night before the test, and you sit down to finish studying the words. Suppose that the rate of memorizing is given by $M^{\prime}(t)=-0.003 t^{2}+0.4 t$, where $M^{\prime}(t)$ is the memory rate, in words per minute. How many words are memorized in the first 14 minutes?
words
Round your answer to the nearest whole word
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Step 1 ：You are memorizing words for a vocabulary test. You studied a few days ago, and you know 23 word already. It is the night before the test, and you sit down to finish studying the words. Suppose that the rate of memorizing is given by \(M'(t)=-0.003 t^{2}+0.4 t\), where \(M'(t)\) is the memory rate, in words per minute.

Step 2 ：To find the total number of words memorized in the first 14 minutes, we need to integrate the rate function from 0 to 14.

Step 3 ：After performing the integration, we find that the total number of words memorized in the first 14 minutes is 58.

Step 4 ：Final Answer: The total number of words memorized in the first 14 minutes is \(\boxed{58}\).