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Chapter 4 Solutions
Calculus: Early Transcendentals (3rd Edition)
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- Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.arrow_forwardCost of employee parking provided by a large firm has been increasing over the years. A business analyst approximates the yearly parking cost by an exponential function. Using P as the yearly parking cost in thousands of dollars and t as the number of years since 2015 (when the firm moved into the current location), the business analyst determines the parking cost function to be P(t) = 65(1.3)' . Find P'(t), the rate at which the parking cost is increasing according to the business analyst's model. Rate of change P'(t) = thousands of dollars/yrarrow_forwardThe initial population size of rock ptarmigans in an area is 500 ptarmigans. The growth rate is 0.2 and the carrying capacity is 8000 ptarmigans. The authorities in the area have announced that it is possible to start hunting in the area when the size of the population has reached 5000 ptarmigans. Assume that time is measured in years. After how many years can a ptarmigan be allowed to hunt in the area if we assume that the population size is in accordance with the logistic equation? )?arrow_forward
- Suppose f ( t ) = 120 ( 1.035 ) t models the population of a city (in thousands) t years from now. This model predicts the population of the city will increase. True or False?arrow_forwardThis exercise uses the radioactive decay model. The half-life of cesium-137 is 30 years. Suppose we have a 14-g sample. (a) Find a function m()- me2h that models the mass remaining after t years mt) - 14(2)) (b) Find a function m(t) = me that models the mass remaining after t years. (Round your rvalue to four decimal places.) m(t) = (c) How much of the sample will remain after 79 years? (Round your answer to one decimal place.) (d) After how many years will only 2g of the sample remain? (Round your answer to the nearest whole number.) yrarrow_forwardSuppose a species of fish in a particular lake has a population that is modeled bythe logistic population model with growth rate k, carrying capacity N, and time tmeasured in years. Adjust the model to account for each of the following situations. * One hundred fish are harvested each year.* One-third of the fish population is harvested annually.* The number of fish harvested each year is proportional to the square root of thenumber of fish in the lake. I was hoping to compare my answer to yours because I am a little confused if I did it right. Thank you for your time and effort.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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