   Chapter 4.5, Problem 83E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Learning Theory Students in a learning theory study were given an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are shown in the table, where t is the time in months after the initial exam and s is the average score for the students. t 1 2 3 4 5 6 S 84.2 78.4 72.1 68.5 67.1 65.3 Spreadsheet at LarsonAppliedCalculus.com(a) Use a graphing utility to find a logarithmic model for the average score s in terms of the time t.(b) Use a graphing utility to plot the data and graph the model. How well does the model fit the data?(c) Find the rates of change of s with respect to t when t = 2 and t = 5.(d) Interpret the meaning of the rates of change found in part (c) in the context of the problem.

(a)

To determine

To calculate: The logarithmic model for the average score s with respect to time t in months in an exam of learning theory study students which is retested in every six months and the table shows the average score s at various months t after the initial exam for the students using graphing utility.

 t 1 2 3 4 5 6 s 84.2 78.4 72.1 68.5 67.1 65.3
Explanation

Given Information:

The table shows the average score s at various months t after the initial exam for the students.

 t 1 2 3 4 5 6 s 84.2 78.4 72.1 68.5 67.1 65.3

Calculation:

Consider the table.

 t 1 2 3 4 5 6 s 84.2 78.4 72.1 68.5 67.1 65.3

Steps to evaluate the logarithmic model using T 183 graphing utility:

Step 1: Press “ON” button.

Step2: Press “STAT” and then “EDIT”.

Step 3: Enter the value of t in L1 and s in L2

(b)

To determine

To graph: The sketch of logarithmic model for the average score s with respect to time t in months with the help of provided table and by using graphical utility.

 t 1 2 3 4 5 6 s 84.2 78.4 72.1 68.5 67.1 65.3

(c)

To determine

To calculate: The rate of change of s with respect to time t when t=2 and t=5 if s is the average score with respect to time t in months with the help of provided table,

 t 1 2 3 4 5 6 s 84.2 78.4 72.1 68.5 67.1 65.3

(d)

To determine

The meaning of rate of change of s with respect to time t when t=2 and t=5 if s is the average score with respect to time t in months with the help of provided table,

 t 1 2 3 4 5 6 s 84.2 78.4 72.1 68.5 67.1 65.3

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 49-62, find the indicated limit, if it exists. 57. limx2x2x6x2+x2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 23-58, perform the indicated operations and simplify. 38.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: f(x) = 4x2 8x + 1 is increasing on (0, 1).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 