A particular region has a rabbit population of 1600. Two foxes are introduced to control the population of rabbits. Following this, the number of rabbits decreases according to the formula R(t) = 1700 – Aekt. where A and k are constants, and R(t) is the number of rabbits in the region t years after the introduction of the foxes. (a) Given that the population of rabbits drops by one quarter after 5 years, find the values of A and k. (b) Following this model, how long will it take for the rabbits to become extinct? Give your answer to two decimal places. (c) Let F(t) be the number of foxes in the region t years after their introduction. If dF = 0.7F(t), dt find the time at which the rate of decrease of the rabbit population is equal to the rate of increase of the fox population, correct to two decimal places. dF and dt dR Hint. Note that represent the rates of change of the rabbit and fox dt populations respectively.

A particular region has a rabbit population of 1600. Two foxes are introduced to control the population of rabbits. Following this, the number of rabbits decreases according to the formula R(t) = 1700 – Aekt. where A and k are constants, and R(t) is the number of rabbits in the region t years after the introduction of the foxes. (a) Given that the population of rabbits drops by one quarter after 5 years, find the values of A and k. (b) Following this model, how long will it take for the rabbits to become extinct? Give your answer to two decimal places. (c) Let F(t) be the number of foxes in the region t years after their introduction. If dF = 0.7F(t), dt find the time at which the rate of decrease of the rabbit population is equal to the rate of increase of the fox population, correct to two decimal places. dF and dt dR Hint. Note that represent the rates of change of the rabbit and fox dt populations respectively.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: The population of the world is given approximately by f(t) = 7.38e0.0119t billion people, where t is…

A: Use the help of derivative and solve the problem.

Q: Newton's law of cooling says that a hot object cools rapidly when the difference between its…

Q: truck plans to drive from a town in state A, to a town in state B. she will drive 84 miles in state…

A: As per the bartleby guidelines for more than three part only three has to be solved please upload…

Q: Two people run for 13 seconds with velocity functions vi = a m/s for person A and vz = 3/Tm/s for…

A: Topic = Algebra

Q: The predator satiation model for population growth specifies that the reproductive rate of an…

Q: In a study of a marine tubeworm, scientists developed a model for the time T (measured in years)…

A: Given, Time required for the tube worm to reach a length is, T=20ebL-28b, where T is in years and L…

Q: (a) Using the multiple linear regression approach (generalized least squares method), write the…

A: a) Using multiple linear regression and given data the model is written in the general form as…

Q: A person’s blood alcohol content (BAC) is a measure of how much alcohol is in the bloodstream. When…

Q: where p(t) is the proportion of the population that knows the rumor at time t and a and k are…

Q: Beth makes a deposit into an account which credits interest at a nominal interest rate of 9% per…

A: Amount of the deposit at maturity includes the principal and interest. After the maturity period,…

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

Q: If r = 0.05 and H = 500, for what values of p0 is the amount ofthe resource decreasing? For what…

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: Assume that from 1860 to 1920, the city of Painesville’s population experienced uninhibited growth.…

Q: Solve the following problem: Suppose a student is a carrier of the flu virus and returns to his…

A: Total number of students=1000 x(4)=50 Determine the number of students long after 7 days ?

Q: Ohm’s law says that the current, I, (in amps) obeys the formula I =V/R where V represents the…

Q: The amount of doxycyclin (an antibiotic) decays rapidly in the blood. If a patient takes 200 mg of…

A: a) Patient takes 200 mg of Oxycontin, so f(0)=Ab0200=A Now, after 5 hours she has only 50 mg, so…

Question

A particular region has a rabbit population of 1600. Two foxes are introduced to
control the population of rabbits. Following this, the number of rabbits decreases
according to the formula
R(t) = 1700 – Aekt.
-
where A and k are constants, and R(t) is the number of rabbits in the region t years
after the introduction of the foxes.
(a) Given that the population of rabbits drops by one quarter after 5 years, find
the values of A and k.
(b) Following this model, how long will it take for the rabbits to become extinct?
Give your answer to two decimal places.
(c) Let F(t) be the number of foxes in the region t years after their introduction. If
dF
= 0.7F(t),
dt
find the time at which the rate of decrease of the rabbit population is equal to
the rate of increase of the fox population, correct to two decimal places.
dR
dF
Hint. Note that
and
represent the rates of change of the rabbit and fox
dt
dt
populations respectively.
(d) Identify any problems with this model.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step by step

Solved in 8 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Indefinite Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The rate of U.S. per capita sales of bottled water for the period 1993-2003 could be approximated by Q(t) = 0.05r +0.41 +9 where t is the time in years since 1990. Compute the average annual sales of bottled water over the period 1996-2003, to the nearest gallon per year. O a. 15 gallons per year b. 17 gallons per year O c. 16 gallons per year O d. 18 gallons per year е. 19 gallons per year
In a city with a fixed population N, the time rate of change of the number P of people who have heard a certain rumor is proportional to the produc of P and NP. Suppose initially 25% have heard the rumor and after one week this number has grown to 50%. What percentage will this number reach after one more week? After one more week, the percentage is %. Your final answer needs to be a fraction. Also, keep in mind that we are working with percent. Submit
b The number of liters of blood pumped through the lungs in one minute is given by C = where b is quantity of oxygen used by the body in one minute, a is the quantity of oxygen per liter of a-v blood that has just gone through the lungs, and v is the quantity of oxygen per liter of blood that is about to enter the lungs. Suppose a = 160, b=205, and v= 125. Estimate the change in C if a becomes 150, b becomes 200, and v changes to 125. Find the equation for the total differential of C to estimate the change in C. dC=da+db + dv
On a monthly basis, when a factory employs L worker-hours of labor, they can produce Q(L) = 7L + 40L/6 scooters. An investment in labor of K dollars gives them an employment level of L(K)=0.055K – 12,500 K worker-hours. The factory currently invests 2,000 dollars in labor. At what rate is the number of scooters being produced changing with respect to the amount they invest in labor? Round your final answer to 2 decimal places and include units with your answer. а.
(b) Towns A and B are 12 km apart. A cyclist leaves A and travels to B at an average speed of y km/h. From B, he returns immediately to A with an average speed reduced by 2 km/h. (i) Find, in terms of y, the time taken for the journey from A to B. (ii) Find, in terms of y, the time taken for the return journey. (iii) Given that the total time spent to travel from A toB and back to A is 5 hours, write an equation satisfied by y. (iv) Solve the equation written in part (iii). (v) Give a simple reason why one of the values of y obtained in part (iv) is not valid.
In order to keep the songbirds in the back yard happy, one person puts out 14g of seeds at the end of each week. During the week, the birds find and eat 70% of the seeds. The DTDS for the amount of seeds in the back yard at time t where t is measured in weeks and seeds are counted just after a new supply is given by Xt+1 = 0.3х, + 14 Which of the following is an equation for the general solution of this DTDS, based on an initial seed quantity of 50g? None of the above/below Xt = (0.7)'(50) + 50 Xị = (0.3)'(30) + 64 Xt = (0.3)'(30) + 20 X; = (14)'(50) + 20 Xị = (0.7)'(30) + 20 = lx
A pan of boiling water with a temperature of 212°F is set in a bin of ice with a temperature of 32°F. The pan cools to 65°F in 33 minutes. (a) Find To, D, and a so that T(t) = T₁ + Dat models the data, where t is in hours. (b) Find the temperature of the pan after 15 minutes. (c) How long did it take the pan to reach 35°F? Support your result graphically. (a) To (Round to the nearest integer as needed.) =
Use the following rates and payments table. Monthly Rate 1 1 2 % 1% Unpaid balance Up to $500 Over $500 New balance Under $200 Over $200 Minimum payment $10 5% of new balance PreviousBalance NewPurchases $346 $70 Find the following. (Round your answers to the nearest cent.) (a) the finance charge for the month$ (b) the new balance$ (c) the minimum monthly payment$