A model for a certain population P(t) is given by the initial value problemdPP(10¬4 – 10-11 P), P(0) = 500000,dt=where t is measured in months.(a) What is the limiting value of the population?(b) At what time (i.e., after how many months) will the populaton be equal to one fifth of the limiting value in(a)?(Do not round any numbers for this part. You work should be all symbolic.)

Answered: Image /qna-images/answer/a9df9b3c-d892-4dcc-8d3d-47bb1988213f.jpg

Answered: A model for a certain population P(t)…

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

Similar questions

Question 1 Revenue function. The weekly marginal revenue from the sale of x pairs of tennis shoes is given by 200 x + 1 where R(x) is revenue in dollars. Find the revenue from the sale of 1,000 pairs of shoes. A. R(1000)=30000 + 200In(1001) B. R(1000) = 20000 + 200ln(1001) c. R(1000) = 30200 D. R'(x)= 40 - 0.02x + R(1000)=20+ 200 1001 R(0) = 0
Suppose the Consumer Price Index. (CPI), can be modeled by the following equation between the years 2000 and 2019: CPI(1) = 200 – 10te – 100e 0
SOLVE THE QUESTION
(4).
3.
Question 2 A patient takes d mg of medicine every 8 hours. Every 8 hours, 80% of the medicine in the patient's bloodstream is eliminated. The medicine has side effects if there is ever 15 mg or more in the patient's blood, but there needs to be at least 2 mg in the patient's blood for it to be effective. (a) What is the maximum safe value for d? (Hint: Consider An, the amount of medicine in the patient's blood immediately after taking the nth dose, and think about what must be true about An to ensure a safe dosing schedule. Write out very carefully what A1, A2, A3 are before trying to find a pattern for An.) (b) What is the minimum effective value for d? (Hint: Consider Bn, the amount of medicine in the patient's blood immediately before taking the nth dose.)
1. A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They concluded that the rate of increase of the fish population is directly proportional to the population at that time, p(t) as well as to the difference between species' carrying capacity and the current population. The carrying capacity for this fish species in the lake was estimated to be 1000. It was observed that the number of the fish tripled in the first year. What would be the fish population in 5 years?

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS