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It is known that there are 10000 cods in Koorsala, and that the cod population there...
It is known that there are 10000 cods in Koorsala, and that the cod population there obeys the logistic model with harvesting. The per capita birth rate of these cods is 14% per year. The people of Koorsala has been catching 400 cods per year for a long time. One year, some advanced fishing equipment is introduced, which increases the harvesting rate to 550 cods per year. Assuming that the Koorsala people carry on with this increased harvesting rate, what will the size of the cod population be in the long run? Give your answer correct to the nearest integer.
Solutions
Expert Solution
After 22 years the growth percentage cod population will be stable at 14% as per the working given below:
| Year | Total | Cod in crease with 14% | Harvesting @ 550 | growth per year | % of growth |
| 1 | 10000 | 11400 | 10850 | ||
| 2 | 10850 | 12369 | 11819 | 969 | 9% |
| 3 | 11819 | 13474 | 12924 | 1105 | 9% |
| 4 | 12924 | 14733 | 14183 | 1259 | 10% |
| 5 | 14183 | 16169 | 15619 | 1436 | 10% |
| 6 | 15619 | 17805 | 17255 | 1637 | 10% |
| 7 | 17255 | 19671 | 19121 | 1866 | 11% |
| 8 | 19121 | 21798 | 21248 | 2127 | 11% |
| 9 | 21248 | 24223 | 23673 | 2425 | 11% |
| 10 | 23673 | 26987 | 26437 | 2764 | 12% |
| 11 | 26437 | 30138 | 29588 | 3151 | 12% |
| 12 | 29588 | 33730 | 33180 | 3592 | 12% |
| 13 | 33180 | 37825 | 37275 | 4095 | 12% |
| 14 | 37275 | 42494 | 41944 | 4669 | 13% |
| 15 | 41944 | 47816 | 47266 | 5322 | 13% |
| 16 | 47266 | 53883 | 53333 | 6067 | 13% |
| 17 | 53333 | 60800 | 60250 | 6917 | 13% |
| 18 | 60250 | 68685 | 68135 | 7885 | 13% |
| 19 | 68135 | 77674 | 77124 | 8989 | 13% |
| 20 | 77124 | 87921 | 87371 | 10247 | 13% |
| 21 | 87371 | 99603 | 99053 | 11682 | 13% |
| 22 | 99053 | 112921 | 112371 | 13317 | 13% |
| 23 | 112371 | 128102 | 127552 | 15182 | 14% |
| 24 | 127552 | 145410 | 144860 | 17307 | 14% |
| 25 | 144860 | 165140 | 164590 | 19730 | 14% |
| 26 | 164590 | 187633 | 187083 | 22493 | 14% |
| 27 | 187083 | 213274 | 212724 | 25642 | 14% |
| 28 | 212724 | 242506 | 241956 | 29231 | 14% |
| 29 | 241956 | 275830 | 275280 | 33324 | 14% |
| 30 | 275280 | 313819 | 313269 | 37989 | 14% |
| 31 | 313269 | 357126 | 356576 | 43308 | 14% |
| 32 | 356576 | 406497 | 405947 | 49371 | 14% |
| 33 | 405947 | 462780 | 462230 | 56283 | 14% |
| 34 | 462230 | 526942 | 526392 | 64162 | 14% |
| 35 | 526392 | 600087 | 599537 | 73145 | 14% |
| 36 | 599537 | 683472 | 682922 | 83385 | 14% |
| 37 | 682922 | 778531 | 777981 | 95059 | 14% |
| 38 | 777981 | 886898 | 886348 | 108367 | 14% |
| 39 | 886348 | 1010437 | 1009887 | 123539 | 14% |
| 40 | 1009887 | 1151271 | 1150721 | 140834 | 14% |
| 41 | 1150721 | 1311822 | 1311272 | 160551 | 14% |
| 42 | 1311272 | 1494850 | 1494300 | 183028 | 14% |
| 43 | 1494300 | 1703503 | 1702953 | 208652 | 14% |
| 44 | 1702953 | 1941366 | 1940816 | 237863 | 14% |
| 45 | 1940816 | 2212530 | 2211980 | 271164 | 14% |
| 46 | 2211980 | 2521657 | 2521107 | 309127 | 14% |
| 47 | 2521107 | 2874062 | 2873512 | 352405 |
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