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

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

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

See similar textbooks

Similar questions

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.
The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning