Urgently need the answers. Please give right answers.
Urgently need the answers. Please give right answers. Q2 Fish Population In this question, we will...
Q2- Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per year is P'(t): P'(t) birth rate - death...
step by step please
4. Suppose that the logistic equation dt Pla -bP) models a population of fish in a lake after t months during which no fishing occurs. What is the limiting population for this fish population? suppose that, because of fishing, fish are removed from the lake at a rate proportional to the existing fish population. i. Write a differential equation that describes this situation. ii. Show that if the constant of proportionality for the harvest of fish,...
Population Growth: Let P(t) be the number of rabbits in the
rabbit population. In the simplest case we can assume the number of
rabbits born at any moment of time is proportional to the number of
rabbits at this moment of time. Mathematically we can write this as
a differential equation:
Here b is the birth rate, i.e. births per time unit per rabbit.
In the model above we ignore deaths and assume resources are
unlimited.
A. Solve the equation...
Consider the differential equation for , which models a population of fish with harvesting that is governed by the logistic equation and a number of fish H caught and removed every unit of time (harvesting). Here the parameters r, K, and H are all positive. a) Assume that . Draw the phase plane. b) Assume that . What happens to the population of fish as t increases? Can I have a step-by-step walkthrough on how to solve these two. I...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answe terms Po, a, k and a constant C.) wer must contain the...
12 10 marks] Algae is growing in a fish tank. The biomass z(t) of the algae at time t is modelled by the Malthusian model dz dt = (b-d)2. Suppose that we buy a chemical that is intended to reduce the amount of algae. If the dosage of the chemical is p, then the birth and death rates of the algae are affected as follows: d(p)=2 and p) (a) On the same set of axes, sketch the graphs of the...
part d please
We go back to the logistic model for population dynamics (without harvesting), but we now allow the growth rate and carrying capacity to vary in time: dt M(t) In this case the equation is not autonomous, so we can't use phase line analysis. We will instead find explicit analytical solutions (a) Show that the substitution z 1/P transforms the equation into the linear equation k (t) M(t) dz +k(t) dt (b) Using your result in (a), show...
6. 0.2/1 points | Previous Answers SCalcET8 9.4.009 My Notes Ask Your Suppose the population of the world was about 6.4 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 20 billion (a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity,...
please complete the whole question
4. A population P of organisms dies at a constant rate of a organisms per unit time, and the growth rate is proportional to the population size with the proportionality constant k A. Assume the initial population P(0) = Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answer must contain the terms Po,...