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BMAD

City Growth

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BMAD    62

A town's population of size x doubled after 30 years (2x).  How long ago was this population 1/2x?

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5 answers to this question

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araver    10
Spoiler

If the population growth is susceptible to be modelled as exponential growth with a constant rate of growth then the answer is 30 years ago, as the doubling time is constant.

Or as an example would show it visually. 

Growth Rate 2.33739%    
         
X 100.0000   X 100.0000
X+1 102.3374   X-1 97.7160
X+2 104.7294   X-2 95.4842
X+3 107.1773   X-3 93.3033
X+4 109.6825   X-4 91.1722
X+5 112.2462   X-5 89.0899
X+6 114.8698   X-6 87.0551
X+7 117.5548   X-7 85.0667
X+8 120.3025   X-8 83.1238
X+9 123.1144   X-9 81.2252
X+10 125.9921   X-10 79.3700
X+11 128.9370   X-11 77.5572
X+12 131.9508   X-12 75.7858
X+13 135.0350   X-13 74.0549
X+14 138.1913   X-14 72.3635
X+15 141.4214   X-15 70.7107
X+16 144.7269   X-16 69.0956
X+17 148.1098   X-17 67.5175
X+18 151.5717   X-18 65.9754
X+19 155.1145   X-19 64.4685
X+20 158.7401   X-20 62.9960
X+21 162.4505   X-21 61.5572
X+22 166.2476   X-22 60.1512
X+23 170.1334   X-23 58.7774
X+24 174.1101   X-24 57.4349
X+25 178.1798   X-25 56.1231
X+26 182.3445   X-26 54.8412
X+27 186.6066   X-27 53.5887
X+28 190.9683   X-28 52.3647
X+29 195.4320   X-29 51.1687
X+30 200.0000   X-30 50.0000

 

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bonanova    76
Spoiler

If we can infer (OP does not say so, but ...) the town's population doubles every 30 years,
then it had population (1/2) x 30 years before it had population x.

 

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plainglazed    65
Spoiler

Sixty years.  Perhaps splitting hairs but I'm a word guy.  The OP states that the town's population has already "doubled" (past tense).

 

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BMAD    62
1 hour ago, plainglazed said:
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Sixty years.  Perhaps splitting hairs but I'm a word guy.  The OP states that the town's population has already "doubled" (past tense).

 

I intended your interpretation but came up with a much different answer than the ones reported

On 9/9/2017 at 1:55 PM, araver said:
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If the population growth is susceptible to be modelled as exponential growth with a constant rate of growth then the answer is 30 years ago, as the doubling time is constant.

Or as an example would show it visually. 

Growth Rate 2.33739%    
         
X 100.0000   X 100.0000
X+1 102.3374   X-1 97.7160
X+2 104.7294   X-2 95.4842
X+3 107.1773   X-3 93.3033
X+4 109.6825   X-4 91.1722
X+5 112.2462   X-5 89.0899
X+6 114.8698   X-6 87.0551
X+7 117.5548   X-7 85.0667
X+8 120.3025   X-8 83.1238
X+9 123.1144   X-9 81.2252
X+10 125.9921   X-10 79.3700
X+11 128.9370   X-11 77.5572
X+12 131.9508   X-12 75.7858
X+13 135.0350   X-13 74.0549
X+14 138.1913   X-14 72.3635
X+15 141.4214   X-15 70.7107
X+16 144.7269   X-16 69.0956
X+17 148.1098   X-17 67.5175
X+18 151.5717   X-18 65.9754
X+19 155.1145   X-19 64.4685
X+20 158.7401   X-20 62.9960
X+21 162.4505   X-21 61.5572
X+22 166.2476   X-22 60.1512
X+23 170.1334   X-23 58.7774
X+24 174.1101   X-24 57.4349
X+25 178.1798   X-25 56.1231
X+26 182.3445   X-26 54.8412
X+27 186.6066   X-27 53.5887
X+28 190.9683   X-28 52.3647
X+29 195.4320   X-29 51.1687
X+30 200.0000   X-30 50.0000

 

forgive my lack of parenthesis what I meant for the problem is 1/(2x)

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  • 0

I think I got what the answer is, now that we know it is 1/(2x).

Spoiler

Since x is in the denominator, the answer will depend on what x is. This means the answer I got was an equation.

If y is the amount of years ago, then the answer is: y=(-30 log(2x^2))/log(2)

 

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