A forest has a population of cougars and a population of rabbits. Let æ represent the number ofcougars (in hundreds) above some level, denoted with 0. So r = – 3 corresponds NOT to anabsence of cougars, but to a population that is 300 below the designated level of cougars. Similarly,let y represent the number of rabbits (in hundreds) above a level designated by zero. The followingsystem models the two populations over time:x' =- 0.125x + yy' =- x + 0.125ySolve the system using the initial conditions a(0)O and y(0) = 1.%3Da(t) =y(t) =%3D

We will solve the given differential equations with condition

Answered: A forest has a population of cougars…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Stock in Company A sells for $94 a share and has a 3-year average annual return of $24 a share. The beta value is 1.25. Stock in Company B sells for $83 a share and has a 3-year average annual return of $16 a share. The beta value is 1.12. Derek wants to spend no more than $16,000 investing in these two stocks, but he wants to earn at least $2700 in annual revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy. Derek should buy ? share(s) of stock in company A snd share(s) of stock in company B Please show corner points!
The gestation period of rabbits is about 29 to 35 days. Therefore the population of a form can increase dramatically in a short period of time. The table gives a population of a form we're tea is the time in months and then is the rabbit population.
You want to know if the type of music one listens to while running impacts their speed. You recruit 50 participants. These participants listen to classical music while running two laps on a track. You time how long it takes each person to run those two laps. A week later, the same participants run two laps on the track while listening to country music. You time how long it takes each person to run those two laps. All else held constant, which of the following would increase power? O Use alpha .01. O Reduce participants to 40. O Use a directional hypothesis. O Conduct a between-subjects design.
Gas mileage actually varies slightly with the driving speed of a car (as well as with highway vs. city driving). Suppose your car averages 29 miles per gallon on the highway if your average speed is 48 miles per hour, and it averages 26 miles per gallon on the highway if your average speed is 65 miles per hour. Answer parts (a) and (b) below. a. What is the driving time for a 2300-mile trip if you drive at an average speed of 48 miles per hour? What is the driving time at 65 miles per hour? The driving time at 48 miles per hour is hours. (Type an integer or decimal rounded to two decimal places as needed.) The driving time is at 65 miles per hour is (Round to two decimal places as needed.) b. Assume a gasoline price of $4.43 per gallon. What is the gasoline cost for a 2300-mile trip if you drive at an average speed of 48 miles per hour? What is the gasoline cost at 65 miles per hour? The gasoline cost at 48 miles per hour is $ (Round to two decimal places as needed.) hours. The…
Given the estimated linear model shown below, complete the following computations. y = 13+ 5x, + 3x2 + 4x3 a. Compute y when x, = 16, x2 = 14, and x3 = 11. %3D %3D b. Compute y when x, = 27, x2 = 18, and x3 = 14. c. Compute y when x, = 31, x2 = 27, and x3 =22. d. Compute y when x, = 11, x, = 25, and | X3 = 31. a. y = 179 b. у %3
A researcher is interested in the effects of diazepam on anxiety in rats. She takes a group of 15 female rats and injects them with 0.005 mg of diazepam for every 100 g the rats weigh, and takes a different group of female rats and injects them with saline. She then puts them all on an elevated-plus maze for 15 minutes and observes how long they spend (in seconds) in the enclosed arms versus the open arms. The less time they spend in the enclosed arms means they have less anxiety. She also weighs them before the injection to make sure she gets the dosage correct. a. Identify the population of interest b. Identify the Independent variable. c. Identify the Dependent variable. d. What scale of measurement was used for the independent variable? Explain why you think so. e. Was the independent variable discrete or continuous? Explain why you think so. f. What scale of measurement was used for the dependent variable? Explain why you think so. g. How could you change the dependent measurement…
The cost of a certain unlimited texting plan from a mobile phone company includes an initiation fee of $40 plus $15 per month. Ify represents the total cost of the plan and x represents the number of months, which equation models this relationship? O y = 55x O y = 15 + 40x O y = 40 + 15x O y = x(40 +15) INTL 9 10:27
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