Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.007t + 0.2t, where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 14 minutes? words

Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.007t + 0.2t, where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 14 minutes? words

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.007t + 0.2t, where
M'(t) is the memory rate, in words per minute. How many words are memorized in the first 14 minutes?
words

Expert Solution

Step 1

The rate of memorizing is given by

$M' (t) = - 0.007 t^{2} + 0.2 t$

Integrate both the sides

$\int M' (t) = \int (- 0.007 t^{2} + 0.2 t) M (t) = - \frac{0.007 t^{3}}{3} + \frac{0.2 t^{2}}{2}$

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