Bacteria are often grown on agar plates and form circular colonies. The area of a colony is proportional to the number of bacteria itcontains. The agar (a gelatinous substance obtained from red seaweed) is the resource that bacteria use to reproduce and so only thosebacteria on the edge of the colony can produce new offspring. Therefore the population dynamics are Nt+1 Nt + I, where I is the inputof new individuals and is proportional to the circumference of the colony, with proportionality constant R. Let the area of the colony bedirectly proportional to the number of bacteria by a constant of proportionality k. Also let K = 2√ K.)(a) Derive the recursion for the population dynamics. (Write your answers in terms of N, Nt, K, and R.)Nt+1=

Answered: Image /qna-images/answer/973d7415-c8f8-4234-807d-e1d40a10809c.jpg

Answered: Bacteria are often grown on agar plates…

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

Find those constants a, b, c, d such that f(z) = ax² + bxy + y? + i(x² + cxy + dy²)
The volume of water in a cylindrical tank is given by: V = лr²h where V is the volume of water in m³, r is the radius of the tank in metres, and h is the height of the water in metres. For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is a constant. Water is filling the tank, so the height and volume are constantly changing hence h and V are variables. At a certain point in time, the height of the tank is increasing by 0.21 metres/hour and the height is 29 metres. Determine the rate of change of volume (in units of m³/h) at this point in time. Give your answer to three decimal places. Hint 1: You are being asked to find dv/dt. Hint 2: dh/dt = 0.21 m/h
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. island 4 km 16 km W L D nest @ A bird with these tendencies is released from an island that is 4 km from the nearest point B on a straight shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Points B and D are 16 km apart. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. (Round your answers to two decimal places.) (a) In general, if it takes 1.2 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively.…
In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were treated with a chemotherapy drug called Cisplatin. If the volume of one of these tumors at the time of treatment is Vo, then the volume of the tumor t days after treatment is modeled by the function V(t) = = Vo(0.99e- + 0.01e0.239t). -0.1216t 1. Set Vo = 3 and plot V(t) over the interval 0 ≤ t ≤ 16. Appropriately adjust the viewing window to see the behavior of V(t) and sketch the graph below. 2. From the graph, estimate the time at which the volume of the tumor decreased to half its original amount. There are two such times, record each to the nearest whole number. 3. With Vo = 3, write down the equation whose solution gives the time at which the tumor is half its original volume. (Re)write the equation with zero in the right-hand side. 4. Using one of your answers from 2. as to and your equation from 3., apply two steps of Newton's method to better approximate this time. (Round to 3 decimal…
While shopping for an air conditione, a buyer bonsulted the following table giving a machine's BTUS and the square footage ( that it would cool t' (x) BTUS (y) 5100 5400 6350 6700 7275 7825 8300 8550 9750 9900 150 175 230 250 285315 350 360 435 | 450 (a) Find a linear model for the data. (b) Use the results from part (a) to find the number of BTUS required to cool rooms of 360 ft, 435 r, and 450 (c) Suppose a room measures 215 Use the results from part (a) to decide how many BTUS it requires if the air conditioners are available only with the BTU cholces in the table, which is the best choice? (a) Find a linear model for the data Find the least-aquares regression ine Once you have found the line in ynix+b form, input the values of m and b into the appropriate boxes below A linear model for the data is y (Round to the nearest whole number as needed) %3D
D Use a linear approximation to estimate v10001.

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