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GROWTH OF A FRUIT FLY COLONY A biologist has determined that the maximum number of fruit flies that can be sustained in a carefully controlled environment (with a limited supply of space and food) is 400. Suppose that the rate at which the population of the colony increases obeys the rule
where C is the carrying capacity (400) and Q denotes the number of fruit flies in the colony at time t. If the initial population of fruit flies in the experiment is 10 and it grows to 45 after 10 days, determine the population of the colony of fruit flies at the end of the 20th day.
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Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
- Grazing Rabbits and Sheep This is a continuation of Exercise 21. In addition to the kangaroos, the major grazing mammals of Australia include merino sheep and rabbits. For sheep, the functional response is S=2.82.8e0.01V, and for rabbits, it is H=0.20.2e0.008V, Here S and H are the daily intake measured in pounds, and v is the vegetation biomass measured in pounds per acre. a. Find the satiation level for sheep and that for rabbits. b. One concern in the management of rangelands is whether the various species of grazing animals are forced to complete for food. It is thought that competition will not be a problem if the vegetation biomass level provides at least 90 of the satiation level for each species. What biomass level guarantees that competition between sheep and rabbits will not be problem?arrow_forwardDecay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forward
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