No SIM ?15:1954%A colstate.view.usg.eduProblem 1:a. A patient has 150 milligrams of aspirin in her bloodstream. If the amount of aspirin inher bloodstream decays exponentially, with one third being removed every 3 hours, findthe amount A(t) of aspirin remaining in the bloodstream after/ hours.31A) A(t) =150B) A(t) = 150C) A(t) =150|D) A(1) =150b. Water that is initially contaminated with a concentration of 9 milligrams of pollutantper liter of water is subjected to a cleaning process. The cleaning process is able to reduce( 3 ),- be the concentration,the pollutant concentration by 25% every 2 hours. Let C(t) = 9in milligrams of pollutant per liter of water t hours after the purification process begins.Find the concentration of pollutant in the water after 5 hours. Please round your answerto two decimal places.A) 2.14 mg/B) 4.38 mg/lC) 0.0088 mg/lD) 0.28 mg/1c. Using the function in part b, when will the concentration of pollutant be 5 milligramsper liter of water? Please round your answer to two decimal places.A) After 0.85 hourD) After 0.42 hoursB) After 2.04 hoursC) After 4.09 hoursProblem 2:Suppose that the displacement d (in meters) of an object at time i (in seconds) satisfiesHarmonic motion with the equation d = 2 sin(2xt)+6.a) What is the maximum displacement from its resting position?А) бmB) 2mC) 8mD) 4mb) What is the period?A) Aв) 2лC) ID) 2c) What is the frequency?A) 1 oscillation / secB) 2 oscillations / secoscillation ( seroscillation /see

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Problem 1: a. A patient has 150 milligrams of aspirin in her bloodstream. If the amount of aspirin in her bloodstream decays exponentially, with one third being removed every 3 hours, find the amount A(t) of aspirin remaining in the bloodstream after/ hours. A) A(1) =150 B) A(1) = 150 C) A(1) =150 - D) A(1) = 150 Water that ie initially contaminated wit fo milligrame of nollutant concentrat

Problem 1: a. A patient has 150 milligrams of aspirin in her bloodstream. If the amount of aspirin in her bloodstream decays exponentially, with one third being removed every 3 hours, find the amount A(t) of aspirin remaining in the bloodstream after/ hours. A) A(1) =150 B) A(1) = 150 C) A(1) =150 - D) A(1) = 150 Water that ie initially contaminated wit fo milligrame of nollutant concentrat

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.1: Logistic Functions

Problem 19E: More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the...

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Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.
More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?
Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.
What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?