v Population Annual Geometric
Population of Annual % Geometric of USA percentage growth
Year Portland(Or) change growth rate Year (in millions) change rate
2012 603026 2012 314.1
2013 609456 1.06 0.01 2013 316.5 0.76 0.01
2014 614628 0.84 0.01 2014 318.9 0.75 0.01
2015 619601 0.80 0.01 2015 320 0.34 0.003
2016 624530 0.79 0.01 2016 324 1.23 0.01
0.87 0.62
Population Annual Geometric
Year USA Percent growth
(Millions) change rate
2012 314.1
2013 316.5 0.76 0.01
2014 318.9 0.75 0.01
2015 320 0.34 0.003
2016 324 1.23 0.01
0.62
Population Annual Geom
Year Portland Percent growth
(OR)
2012 603026
2013 609456 1.06 0.01
2014 614628 0.84 0.01
2015 619601 0.80 0.01
2016 624530 0.79 0.01
0.87
For Portland
We know that Pt = P0 (1+r)t
Here Pt =2 P0
Hence 2P0 = P0 (1+r)t 1
1+r= 1.009 2 2
or 2P0 = P0 * (1+r)t
or 2 = (1+r)t
r = 0.009 2 = 1+.87/100)^t 1.009 ^t 1.009 ^t Output 77 years
Taking logarithms,
log 2 = t log 1.009 1.009
0.3010 = t * 0.0039 0.0039
t = 77 years
0.004321374
Directly 77 years s
For USA
Here Pt =2 P0
Hence 2P0 = P0 (1+r)t P0 (1+r)t 1
2 2
or 2P0 = P0 * (1+r)t P0 * (1+r)t
or 2 = (1+r)t = (1+r)t
r= 0.0062 2 = 1.006 ^t = 1.006 ^t Output 116 years
Taking logarithms,
log 2 = t* log 1.006
0.3010 = t * 0.0026 *
s t = 116 years
Directly 116 years
As the Geometric growth rate is r = >01 .01 for both Portland(OR) and USA the population will double in
70 years
As the growth rate is 1 the exponential growth rate for doubling = 70/r = 70 years
for both Portland(OR) and USA
USA - 2010
Proportion
Married of
Females No. of Never Spouse spinsters n*nSx
n Age group females Married Present nSx
1 0-17 18 18 18
2 18-19 4004 3816 96 0.95305 1.906093906
5 20-24 10465 8296 1708 0.79274 3.963688485
5 25-29 10515 5026 4451 0.47798 2.389919163
5 30-34 9864 2678 5753 0.27149 1.357461476
5 35-39 9982 1768 6362 0.17712 0.885594069
5 40-44 22594 1430 6753 0.06329 0.316455696
10 45-54 18401 2479 14339 0.13472 1.347209391
30.17
∑ n* nSx = 30.17
k= 45
Sk = S45 = (5S40 + 10S45)/2 = 0.099006039
a 45 X' = {{∑n*nSx - k*Sk/(1 - Sk)} = 28.54 years
Mean age at Marriage = 28.54 years
z Note: -Total number of females and Number of unmarried females are taken same from (0-17) years of age group and hence the proportion of spinsters is taken as 1. proportion of spinsters is taken as 1.
Source:- US Census Bureau
2010--USA 2010
Population in 000"
IN '000 No. of births 3999
308745 No. of deaths 2468
Source:National Center Health Statistics
Birth Rate = 12.95
Death Rate = 7.99
Natural increase = 4.96
2010 = US opulation in 2010 US Population 2010 309 (in millions)
US Population 2016 324 (in millions)
No. of Years 7
Rate of growth r = 1%