Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500 in the logistic population model of Exercise 17. Suppose P(0) = 2500. (a) If 100 fish are harvested each year, what does the model predict for the longterm behavior of the fish population? In other words, what does a qualitative analysis of the model yield? (b) If one-third of the fish are harvested each year, what does the model predict for the long-term behavior of the fish population?

A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) =     (b) Plot the graph of the model you found in part (a) over the first 20 years.         (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.

Escherichia coli, commonly referred to as E. coli, is essential for modern biotechnology research. One reason for this is the ease and speed at which E. coli can be cultivated in the laboratory. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in al culture doubles approximately every 15 minutes. Suppose an initial colony of 100 E. coli bacteria are to be used for an experiment. Use the exponential growth model Y = Yekt where t is measured in minutes, to write an exponential growth function for bacteria colony. Round the growth constant (k) to four significant figures. The exponential growth function that models growth of the E. coli colony is Approximately how many bacteria will be present in the colony after 175 minutes? Round the solution to the nearest whole number. Approximately bacteria will be present in the colony after 175 minutes. Determine how long it will take for the bacteria colony to reach 100,000,000…

Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 Population (in millions) 3.929 5.308 7.240 9.638 12.866 17.069 23.192 31.433 38.558 50.156 62.948 75.996 91.972 105.711 122.775 131.669 150.697

The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?

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Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 fish. Absent constraints, the population would grow by 110% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 =   After two breeding seasons the population of the pond is given by�2 =