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Find the relative growth rate.

Assume the relative growth rate is a linear function of population at time t by using the formula . 
(1/p)(dp/dt) = b + at.

Time

T

Population

symmetric difference quotient 

Relative Growth Rate

1790

0

3.9

 

 

1800

10

5.3

0.1650

 

1810

20

7.2

0.2150

 

1820

30

9.6

0.2850

 

1830

40

12.9

0.3750

 

1840

50

17.1

0.5150

 

1850

60

23.2

0.7150

 

1860

70

31.4

0.8300

 

1870

80

39.8

0.9400

 

1880

90

50.2

1.1550

 

1890

100

62.9

1.2900

 

1900

110

76

1.4550

 

1910

120

92

1.4850

 

1920

130

105.7

1.5400

 

1930

140

122.8

1.3000

 

1940

150

131.7

1.4250

 

1950

160

151.3

2.3800

 

1960

170

179.3

2.6000

 

1970

180

203.3

2.3600

 

1980

190

226.5

2.2700

 

1990

200

248.7

2.7450

 

2000

210

281.4

 

 

 

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