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{"ops":[{"insert":"A park has a stable population of birds. Prior to this situation, the birds\u2019 population\nincreased from an initial low level. When the population of birds was 1000, the\nproportionate birth rate was 40% per year and the proportionate death rate was 5% per\nyear. When the population was 3,000, the proportionate birth rate was 30% and the\nproportionate death rate was 10%. Consider the population model under the following\nassumptions:\n(i) There is no migration and no exploitation.\n(ii) The proportionate birth rate is a decreasing linear function of the population.\n(iii) The proportionate death rate is an increasing linear function of the population.\nShow that\nThe population grows according to the logistic model.\nFind the stable population size.\nIf the shooting of birds is allowed at the rate of 15% of the population per year, find the\nnew equilibrium population.\n"}]}
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