   Chapter 3.8, Problem 5E ### 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

# The table gives estimates of the world population, in millions, from 1750 to 2000. (a) Use the exponential model and the population figures for 1750 and 800 to predict the world population in 1900 and 1950. Compare with the actual figures.(b) Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. Compare with the actual population.(c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. Compare with the actual population and try to explain the discrepancy.

(a)

To determine

To compare: The population figures for 1750 and 1800 to predict the world population in 1900 and 1950.

Explanation

Calculation:

The exponential model is P(t)=P0ekt (1)

Let t is the number years and P(t) is the population in t years.

From given table,

In 1750, the value of t=0 and P(0)=790.

In 1800, the value of t=18001750 and P(50)=980.

Substitute P(0)=790 and P(50)=980 in equation (1),

980=790e50k980790=e50ke50k=9879

Take natural logarithm on both sides,

lne50k=ln987950k=ln9879k=ln987950k=0

(b)

To determine

To compare: The population figures for 1850 and 1900 to predict the world population in 1950.

(c)

To determine

To compare: The population figures for 1900 and 1950 to predict the world population in 2000.

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