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Profits An investment services company experienced dramatic growth in the last two decades. The following models for the company’s revenue R and expenses or costs C (both in millions of dollars) are functions of the years past 1990.
(a) Use the models to predict the company’s profit in 2020.
(b) How long before the profit found in part (a) is predicted to double?
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Chapter 5 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- Marine Fishery One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have G=0.3n(1n2)0.1n Here G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish. a.Make a graph of G versus n. include values of n up to 1.5 million tons. b.Use functional notation to express the growth rate if the population size is 0.24 million tons, and then calculate that value. c. Calculate G1.42 and explain in practical terms what your answer means. d.At what population size is the growth rate the largest?arrow_forwardradioactive Decay These exercises use the population radioactive Decay. Radioactive Radium The half life of radium 226 is 1600 years. Suppose we have a 22-mg sample. (a) Find a function m(t)=m02r/k that models mass remaining after t years. (b) Find a function m(t)=m0ert that models the remaining after t years. (c) How much of sample will remain after 4000 years? (d) After how many years Will only 18 mg Of sample remain?arrow_forwardEastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?arrow_forward
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