BMAD 64 Report post Posted September 8, 2017 A town's population of size x doubled after 30 years (2x). How long ago was this population 1/2x? Quote Share this post Link to post Share on other sites
0 araver 10 Report post Posted September 9, 2017 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 Quote Share this post Link to post Share on other sites
0 bonanova 84 Report post Posted September 11, 2017 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. Quote Share this post Link to post Share on other sites
0 plainglazed 67 Report post Posted September 11, 2017 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). Quote Share this post Link to post Share on other sites
0 BMAD 64 Report post Posted September 11, 2017 1 hour ago, plainglazed said: Hide contents 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: Hide contents 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) Quote Share this post Link to post Share on other sites
0 Buddyboy3000 4 Report post Posted September 11, 2017 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) Quote Share this post Link to post Share on other sites
A town's population of size x doubled after 30 years (2x). How long ago was this population 1/2x?
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