   Chapter 2.3, Problem 61E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Population Aging The following table shows the percentage of U.S. residents over the age of 65 in 1950, 1960, …, 2010:38 Year t (years since 1900) 50 60 70 80 90 100 110 Percentage P over 65 (%) 8.2 9.2 9.9 11.3 12.6 12.6 13 a. Find the logarithmic regression model of the form P ( t ) = A ln t + C . (Round the coefficients to four significant digits). [HINT: See Example 4.]b. In 1940, 6.9% of the population was over age 65. To how many significant digits does the model reflect this figure?c. Which of the following is correct? The model, if extrapolated into the indefinite future, predicts that(A) The percentage of U.S. residents over the age of 65 will increase without bound.(B) The percentage of U.S. residents over the age of 65 will level off at around 14.2%.(C) The percentage of U.S. residents over the age of 65 will eventually decrease.

(a)

To determine

To calculate: The logarithmic regression model of the form P(t)=Alnt+C for the following table that shows the percentage of U.S. residents over the age of 65 since 1950,

 Year t (year since 1900) 50 60 70 80 90 100 110 Percentage P over 65(%) 8.2 9.2 9.9 11.3 12.6 12.6 13
Explanation

Given Information:

The given table is,

 Year t (year since 1900) 50 60 70 80 90 100 110 Percentage P over 65(%) 8.2 9.2 9.9 11.3 12.6 12.6 13

Calculation:

Consider the table,

 Year t (year since 1900) 50 60 70 80 90 100 110 Percentage P over 65(%) 8.2 9.2 9.9 11.3 12.6 12.6 13

To find the logarithmic regression model use T-83 calculator and follow the blow steps,

Step 1: Use STAT EDIT to enter the value of the table.

 L1 L2 60 70 80 90 100 110 9

(b)

To determine

The number of significant digits reflected by the percentage of population of age over 65 in U.S. in 1940.

(c)

To determine

The correct statement form the following options,

(A) The percentage of U.S. residents over the age of 65 will increase without bound.

(B) The percentage of U.S. residents over the age of 65 will level off at around 14.2%.

(C) The percentage of U.S. residents over the age of 65 will eventually decrease.

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