Problem

Suppose that in a memory experiment the rate of memorizing is given by \[ M^{\prime}(t)=-0.003 t^{2}+0.8 t \] where $M^{\prime}(t)$ is the memory rate, in words per minute. How many words are memorized in the first $20 \mathrm{~min}$ (from $t=0$ to $\mathrm{t}=20) ?$ In the first 20 minutes words are memorized.

Solution

Step 1 :Suppose that in a memory experiment the rate of memorizing is given by \(M'(t)=-0.003 t^{2}+0.8 t\), where \(M'(t)\) is the memory rate, in words per minute.

Step 2 :To find the total number of words memorized in the first 20 minutes, we need to integrate the rate function from 0 to 20.

Step 3 :After performing the integration, we find that the total number of words memorized in the first 20 minutes is 152.

Step 4 :Final Answer: The total number of words memorized in the first 20 minutes is \(\boxed{152}\).

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Source: https://solvelyapp.com/problems/7944/

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