Population growth of any species is frequently modeled by an ODE of the form where N is the population, aN represents the birthrate, and bN2 represents the death rate due to all causes, such as disease, competition for food supplies, and so on. If N0 = 100,000, a = 0,1, and b = 0.00008, calculate N(t) using fourth order Runge-Kutta method for t = 0.0 to 20.0 years with h = 4. Rules: Use any for each of the problem in five decimal places.

Population growth of any species is frequently modeled by an ODE of the form where N is the population, aN represents the birthrate, and bN2 represents the death rate due to all causes, such as disease, competition for food supplies, and so on. If N0 = 100,000, a = 0,1, and b = 0.00008, calculate N(t) using fourth order Runge-Kutta method for t = 0.0 to 20.0 years with h = 4. Rules: Use any for each of the problem in five decimal places.

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

Related questions

Q: In a M/M/1 model, and the average time a customer waits in the system is 0.75 hour, and the average…

Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

A: The logistic equation describes the growth of a certain population of fish in a pond.The pond's…

Q: An experiment is to be conducted examining the growth rate of juvenile coho salmon under different…

A: The objective of the question is to calculate the total number of fish required for the experiment.…

Q: Determine exact values for a and b so that the exponential function g(t) = abt passes through the…

A: We find a and b so that the exponential function g(t) = abt passes through the points (7, 9) and…

Q: A culture of bacteria obeys the law of uninhibited growth.(a) If N is the number of bacteria in the…

A: (a) In uninhibited growth the population at time t is given by an exponential function of the form…

Q: A population of a town grows according to the law of uninhibited growth modeled by the function P(t)…

Q: idemic and oxen) epidemic called epizooty. The estimated number of new cases every 28 days is listed…

Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

A: The objective of this question is to calculate the population of fish in a pond after one and two…

Q: In a printing shop, print requests arrive randomly and independently at an average rate of 20 per…

A: i).Given:Time taken for 1 request=1.25Thus, time taken for 5 request=1.25*5=6.25 The formula and…

Q: A firm's annual sales rise from 50 000 to 55 000 from one year to the next. Express the rise as a…

Q: If a pesticide released during a dawn (6 am) crop spraying event is present at 55 mg/L in a pond…

A: To find the rate constant for the degradation of the pesticide, we need to first find the…

Q: Below are data on the population of a species of moths that inhabit an island and breed annually…

Q: Which of the following population models predicts a population that reaches a carry capacity? There…

A: Population reaches carrying capacity when number of people remains the same over a period of time.…

Q: (a) find the value of A and a, correct to 3 decimal places, (b) predict the percentage of…

A: Topic:- exponential function

Q: A room is equipped with four led light bulbs. The lighting system is programmed so that one led bulb…

A: From the given information, A room is equipped with four led light bulbs. The lifetime of each bulb…

Q: A function of the form P(t) =ab' represents the population (in millions) of the given country t…

A: The main objective is to convert the function of the form, Pt=abt into the function of the form…

Q: Suppose variable Y measures financial ratings A : y = 1, B : y = 2, and C : y = 3, that is, the…

A: The random variable measures financial ratings representing creditworthiness, where A is high, B…

Q: 5. Order the following functions according to their order of growth (from the lowest to the…

A: Introduction: The term "order of growth" refers to the rate at which a function's value increases or…

Q: Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics…

Q: 1. For all types of animals, the percentage that survive into the next year decreases. In one study,…

A: Consider the equation that models the survival rate of the reindeer as,

Q: A scientist is studying three different cultures of bacteria {labeled "A", "B" and "C"} and wants to…

A: For crop type A, the general solution to exponential growth is, e) dP/dt = kP with P(0)=P0 and…

Question

Population growth of any species is frequently modeled by an ODE of the form

where N is the population, aN represents the birthrate, and bN² represents the death rate due to all causes, such as disease, competition for food supplies, and so on. If N₀ = 100,000, a = 0,1, and b = 0.00008, calculate N(t) using fourth order Runge-Kutta method for t = 0.0 to 20.0 years with h = 4.

Rules: Use any for each of the problem in five decimal places.

Population growth of any species is frequently modeled by an ODE of the form
dN
- = aN - bN?
dt
N(0) = No
where N is the population, aN represents the birthrate, and bN? represents the death rate due to all
causes, such as disease, competition for food supplies, and so on. If No = 100,000, a = 0,1, and b =
0.00008, calculate N(t) using fourth order Runge-Kutta method for t = 0.0 to 20.0 years with h = 4.
Rules: Use any for each of the problem in five decimal places.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose that we want to build a model that predicts the group membership of a hurricane, either tropical (0) or non-tropical (1) based on the latitude of formation of the huricane. The response variable is the binary variable Type.new (type of hurricane) and the predictor variable is FirstLat (First Latitude). Using R, we build a model by applying the glm () function. For the logistic regression model, we specify family = "binomial". The data is available at https://userpage.fu-berlin.de/soga/200/2010 data sets hurricanes.xlsx. The R code is #set up filename my.filename 1z|) <2e-16 *** 0.96148 -9.446 0.37283 0.03947 9.447 <2e-16 *** --- *# Signif. codes: 0 '*** 0.001 **' 0.01 '*' 0.05'.' 0.1 '' 1 # (Dispersion parameter for binomial family taken to be 1) Null deviance: 463.11 on 336 degrees of freedom *# Residual deviance: 232.03 on 335 degrees of freedom *# AIC: 236.03 *# Number of Fisher Scoring iterations: 6 What is the interpretation of the p-value of the predictor variable…
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=300, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
Chlorophylls a and b are plant pigments that absorb sunlight and transfer the energy into photosynthesis of carbohydrates from CO2 and H2O, releasing O2 in the process. Chlorophylls were extracted from chopped up grass and measured by spectrophotometry. The table shows results for chlorophyll a for four separate analysis of five blades of grass. Chlorophyll a (g/L) Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 1.09 1.26 1.1 1.23 0.85 0.86 0.96 1.21 1.3 0.65 0.93 0.8 1.27 0.97 0.86 0.99 0.73 1.12 0.97 1.03 Four replicate measurements for each blade of grass tell us the precision of the analytical procedure (sanalysis). Differences between mean values for each of the five blades of grass are a measure of variation due to sampling (ssampling). Using Excel and it’s ANOVA function, find the standard deviations attributable to sampling and to analysis, as well as the overall standard deviation arising from both sources.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 2000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
Consider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 - 0.238female + 0.17educ + 0.0232 exper - 0.00058exper? +0.0295tenure – 0.00059tenure? female 1 if the person is female, and 0 if the person is male educ = level of education, in years exper = level of expertise, in years tenure = duration of tenure, in years Given that the above regression model has 313 observations, then its degrees of freedom is equal to For the same levels of education, expertise, and tenure, women earn exactly % less compared to men, holding other factors fixed.
Biologists stock a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 10, 000. The number of fish tripled in the first year.