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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?"
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
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?
5 L A T E S T R E P L I E S (Newest First)
Posted - 09/26/2013 : 19:02:44Yes.
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.
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?
Posted - 09/11/2013 : 14:31:21 My error. This is not an exponential problem but a geometric series problem.
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.