Please show me how to get to the answer 9. A model for the ability M of a child to memorize, measured on a scale from 0 to 10 is given by m = 1+1.6t In t,0 9.a. 2.018b. 8.035

Answered: a. between the child's first and second…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please show me how to get to the answer

9. A model for the ability M of a child to memorize, measured on a scale from 0 to 10 is given by m = 1+
1.6t In t,0 <t< 4, where t is the child's age in years. Find the average value of M.
a. between the child's first and second birthdays.
b. between the child's third and fourth birthdays.

Expert Solution

Step 1

The average value of M between 1st and 2nd birthdays will be:

$\begin{array}{rcl} Avg value & = & \frac{1}{b - a} \int_{a}^{b} M d t \\ = & \frac{1}{2 - 1} \int_{1}^{2} [1 + 1.6 t \ln t] d t \\ = & {[t + 1.6 (\frac{t^{2}}{2} \ln t - \frac{t^{2}}{4})]}_{1}^{2} \\ = & [2 + 1.6 (\frac{2^{2}}{2} \ln 2 - \frac{2^{2}}{4})] - [1 + 1.6 (\frac{1^{2}}{2} \ln 1 - \frac{1^{2}}{4})] \\ = & 2.01807 \end{array}$

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