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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The table gives the population of the world P(t), in millions, where t is measured in years and t = 0 corresponds to the year 1900.

t
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

(a) Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant fines.

(b) Use a graphing device to find a cubic function (a third- degree polynomial) that models the data.

(c) Use your model in part (b) to find a model for the rate of population growth.

(d) Use part (c) to estimate the rates of growth in 1920 and 1980. Compare with your estimates in part (a).

(e) Estimate the rate of growth in 1985.

To determine

Part (a)

To estimate: The rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines.

Explanation

1) Formula:

slope=y2-y1x2-x1

2) Calculation:

First calculate rate of population growth in 1920.

So, first find slope for secant line between 1910-1920 and 1920-1930. Then find average between them.

Do same process for 1980.For 1920

1860-17501920-1910=11010=11

2070-18601930-1920=21010=21

To determine

Part (b)

To find: a cubic function that models the data.

To determine

Part (c)

To find: a model for the rate of population growth.

To determine

Part (d)

To estimate: the rates of growth in 1920 and1980.

To determine

To estimate: the rate of growth in 1985.

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