1. Suppose a population of bacterial doubles every hour, but that 1×10 individuals are removed before reproduction to be converted into valuable biological by- products. Suppose the population begins with b, = 3x10 bacteria. %3D (a) Find the population after 1, 2, and 3 hours. (b) Write the updating function which describes the discrete-time dynamical system.
1. Suppose a population of bacterial doubles every hour, but that 1×10 individuals are removed before reproduction to be converted into valuable biological by- products. Suppose the population begins with b, = 3x10 bacteria. %3D (a) Find the population after 1, 2, and 3 hours. (b) Write the updating function which describes the discrete-time dynamical system.
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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please help me to do the first question,thank you!
Transcribed Image Text:1. Suppose a population of bacterial doubles every hour, but that 1×106 individuals
are removed before reproduction to be converted into valuable biological by-
products. Suppose the population begins with b, = 3x10 bacteria.
(a) Find the population after 1, 2, and 3 hours.
(b) Write the updating function which describes the discrete-time dynamical
system.
2. Find the composition of the following updating function with itself (put things
over a common denominator to simplify the composition), and find the inverse
function.
f(x) =
1+x
%3D
3. Cobweb the following discrete-time dynamical system for five steps starting with
the given initial condition and graph the solutions.
X,1 = 2x, +30 with initial condition x, =0
%3D
4. Find the equilibria of the following discrete-time dynamical system that include
parameters. Identify values of the parameter K for which there is no equilibrium,
for which the equilibrium is negative, and for which there is more than one
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