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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

In Section 1.4 we modeled the world population from 1900 to 2010 with the exponential function

P(t) = (1436.53) · (1.01395)t

where t = 0 corresponds to the year 1900 and P(t) is measured in millions. According to this model, what was the rate of increase of world population in 1920? In 1950? In2000?

To determine

To find: The rate of increase of world population in 1920, 1950 and 2000.

Explanation

Given:

The exponential function p(t)=(1436.53)(1.01395)t.

Calculation:

Obtain the derivative p(t).

p(t)=ddt(p(t))=ddt((1436.53)(1.01395)t)

Using the derivative ddx(ax)=axlna,

p(t)=(1436.53)((1.01395)tln(1.01395))

Given that, in section 1.4 the world population from 1900 to 2010, where t = 0 corresponds to the year 1900.

In the year 1920, the value of t is t=19201900. That is, t=20.

Substitute t=20 in p(t).

p(20)=(1436

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