   Chapter 1.4, Problem 35E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Use a graphing calculator with exponential regression capability to model the population of the world with the data from 1950 to 2010 in Table 1 on page 49. Use the model to estimate the population in 1993 and to predict the population in the year 2020.

To determine

To estimate: The population in 1993 and predict the population in 2020.

Explanation

Given:

The populations from the year 1900 to 2010 is shown below the table.

 t (years since 1900) Population (millions) 0 1650 10 1750 20 1860 30 2070 40 2300 50 2560 60 3040 70 3710 80 4450 90 5280 100 6080 110 6870

Calculation:

From the given table, let 0 corresponds to the year 1900 and 110 corresponds to the year ear 2010.

So the year 1993 corresponds for t=93 and the year 2020 corresponds for t=120.

Consider the several values from the table that is from the year 1950 to 2010.

 50 2560 60 3040 70 3710 80 4450 90 5280 100 6080 110 6870

Using online graphing calculator to draw a graph for the years 1950 to 2010 and the corresponding population is shown below Figure 1.

Using Computer Algebra System, the equation of the model in the year 1950 to 2010 is as follows,

The equation of the model is y=1129.2019×e0.0168t, where t be the years after 1900 and y be the populations in million.

Using online graphing calculator to draw the graph for y=1129.2019×e0.0168t as shown below Figure 2.

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