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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The table gives the population of Indonesia, in millions, for the second half of the 20th century.

Chapter 3.8, Problem 6E, The table gives the population of Indonesia, in millions, for the second half of the 20th century.

(a) Assuming the population grows at a rate proportional to its size, use the census figures for 1950 and 1960 to predict the population in 1980. Compare with the actual figure.

(b) Use the census figures for 1960 and 1980 to predict the population in 2000. Compare with the actual population.

(c) Use the census figures for 1980 and 2000 to predict the population in 2010 and compare with the actual population of 243 million.

(d) Use the model in pan (c) to predict the population in 2020. Do you think the prediction will be too high or too low? Why?

(a)

To determine

To compare: The population figures for 1950 and 1960 to predict the world population in 1980.

Explanation

Calculation:

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

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

From given table,

In 1950, the value of t=0 and P(0)=83.

In 1960, the value of t=19601950 and P(10)=100.

Substitute P(0)=83 and P(10)=100 in equation (1),

100=83e10k10083=e10ke10k=10083

Take natural logarithm on both sides,

(b)

To determine

To compare: The census figures for 1960 and 1980 to predict the world population in 2000.

(c)

To determine

To compare: The population figures for 1980 and 2000 to predict the world population in 2010.

(d)

To determine

To describe: In 2020, the prediction will be too high or too low by using part (c).

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