Author 
Topic 

moon1130
Senior Member
USA
24 Posts 
Posted  09/10/2013 : 01:37:18

Problem:
"Suppose the population of a small country where no one moves away and everyone marries and stays married is 100,000. What will the population be in four generations if every couple has exactly two children?"
My Solution:
I am using the formula A=P(1+r)^t, where P is the beginning population of 100,000, t = the number of generations, and r =2 (doubling of the population per generation). Therefore,
A = 100,000(1+2)^4 = 8,100,000
Question:
I do not think that the rate of increase in population per generation is 200%. How do I determine the correct rate of change in this problem?
Thank yoiu 


moon1130
Senior Member
USA
24 Posts 
Posted  09/10/2013 : 07:56:12

I did the problem over again and tried to determine a value for r. Now the population starts at 100,000. At the end of the 2nd generation we have a population of 100,000 + 200,00 = 300,000. Therefore, 100,000(1+r)^2 = 300,000 (1+r)^2 = 3 1 + r = 3 r = 3  1 = 0.732..
Then A = 100,000(1+0.732)^4 = 900,000
So, after 4 generations, the population will be 900,000.
I would like to know if this solution is correct.
Thank you. 


moon1130
Senior Member
USA
24 Posts 
Posted  09/11/2013 : 14:31:21

My error. This is not an exponential problem but a geometric series problem. 


Ultraglide
Advanced Member
Canada
299 Posts 
Posted  09/23/2013 : 11:46:43

You're right, the increase is not 200% for each generation. If we start with 100 000 people (all in couples) and each couple them have 2 children, then after 1 generation there will be 100 000 x 2 or 200 000 people. The population has obviously doubled. If it doubles in the next generation, there will be 400 000 (100 000 x 2). Can you continue the process? 


moon1130
Senior Member
USA
24 Posts 
Posted  09/26/2013 : 14:40:29

Thanks for your response, Ultraglide. After n generations, the population would be 100,000(2^n). Please let me know if I am incorrect.
Again, thank you very much. 


Ultraglide
Advanced Member
Canada
299 Posts 
Posted  09/26/2013 : 19:02:44

Yes. 



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