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
|
|
|