Population growth Definition and 43 Threads

$\tiny{\textbf{6.8.7}}$ Kiaser HS Population Growth The population of a southern city follows the exponential law (a) If N is the population of the city and t is the time in years, express N as a function of t.$N(t)=N_0e^{kt}$ (b) If the population doubled in size over an 18-month period and...

image to avoid typos Ok I'm clueless,

I want to estimate the number of male and female cattle produced over a period of time (say, five years and ten years) from an initial stock of 30 heifers, all 18 months of age at which age they are first joined (mated). Assume that the first calf is born when the mother is 27 months old...

Hey, I found an interesting algebra problem combined with log. It was quite an unique one so I wanted to share it with you guys. Problem: There is a city where the population increases at a constant rate. At the end of 2016, the population of the city was 2 times larger than the population...

Homework Statement The Pacific halibut fishery has been modeled by the differential equation. \displaystyle\dfrac{dy}{dt}=ky\left(1-\dfrac{y}{M} \right) where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying...

Homework Statement Hey guys I'm struggling to find much information of modelling single species population dynamics that relates to this question. A question like this is going to be coming up in my final exam and I need to be able to solve it. I'm struggling to even know where to start. I'm...

Homework Statement [/B] Summarizing: two civilizations hate each other, one of the civilizations throws a curse at the second. The second civilization succumbs to chaos and has a change in Population each week of ΔP= -√P. That is: Pn = Pn-1-√Pn-1 Homework Equations [/B] Considering that the...

Couldn't figure a better thread title but my question is as follows. Intro... I was bought up to think that any suggestion to limit population growth from a state level is like the most evil suggestion. Given that science will prolly always find ways to feed people I would like to leave food...

Homework Statement A bacteria culture initially contanis 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. a. Find an expression for the number of bacteria after t hours. b. find the number of bacteria after 3 hours c. find the rate of...

1. The population of a certain country grows according to the formula: N = N0e^kt Where N is the number of people (in millions) after t years, N0 is the initial number of people (in millions) and k = 1/20 ln 5/4. Calculate the doubling time of this population. Leave your answer in terms of ln...

1. The Problem In the mythical country of Myland, the population recently reached 10 million. At that time, a popular news magazine predicted that with an average yearly growth rate of 2%, the population would be 20 million in 50 years. How does this value (18 million) compare to the value...

i suck at these kind of problems #1 Suppose a population grows according to a logistic model with initial population 1000 and carrying capacity 10000. if the population grows to 2500 after one year, what will the population be after another three years.#2 a. make a guess as to the carrying...

A bacterial population B is known to have a rate of growth proportional to B itself. If between noon and 2pm the population triples, at what time no controls being exerted, should B becomes 100 times? what it was at noon? using this formula $\displaystyle P(t) \;=\;P_oe^{kt}$ please help me...

αℓєєиα♥'s question at Yahoo! Answers regarding the logistic population growth model Here is the question: I have posted a link there to this topic so the OP can see my work.

Does anyone know how to solve dP/dt = k P - A P2 - h for P. I understand partial fractions are needed and I have already solved dP/dt = k P - A P2. Is anyone able to solve it, Cheers NZBRU.

Homework Statement I'm trying to model how a population would grow wrt the following constraints: 1. Number of people within the population 2. How many people each person of the population informs 3. Probability of each person of the population informing a member outside the population...

Homework Statement A population started at 10,000 in 1900. The population doubles every 50 years. What was the population in 2000? Homework Equations Q(time) = Q(initial)*e(rate)(time) The Attempt at a Solution I was able to come up with the answer using the standard growth...

Homework Statement A biologist prepares a culture. After 1 day of growth the biologist counts 1000 cells. After 2 days he counts 3000. Assuming a Malthusian model what is the reproduction rate and how many cells were present initially. Homework Equations P(t) = Ce^{rt} The...

Would anyone be able to go through some of the steps for these problems? 1. The birth rate in a state is 2% per year and the death rate is 1.3% per year. The current population of the state is 8,000,000. a) Write a differential equation which models the population of the state. Be sure to...

Homework Statement At the beginning of the Gold Rush, the population of Coyote Gulch, Arizona was 365. From then on, the population would have grown by a factor of e each year, except for the high rate of "accidental" death, amounting to one victim per day among every 100 citizens. By solving...

Homework Statement Here is the equation I am given. I'm supposed to find the carrying capacity. dp/dt=.05P-6.6666667e-5P^2 I know the general solution is rp-rp^2/k with k=carrying capacity, but the addition of the middle term has thrown me off. The Attempt at a Solution I tried...

Homework Statement Homework Equations <see above>The Attempt at a Solution I'm a bit unsure how to set this up to solve for a solution. Any advice? Its obviously a separable differential equation. But I'm unsure what it is I'm looking for. This looks different then some population...

For the period from 1900 to 1980, calculate the log base e (ln) of the world population values and plot these values on the vertical axis against the year on the horiontal axis. Draw the best straight line you can through these points and determine its slope, k. What is the exponential...

Homework Statement The population of the world was 5.7 billion people in 1995 and 6.2 billion in 2008. Assuming exponential growth by what year will the population reach 11 billion? The Attempt at a Solution i started by trying to find R but am not sure the my way is right...

Homework Statement Consider a population whose number we denote by P . Suppose that b is the average number of births per capita per year andd is the average number of deaths per capita per year. Then the rate of change of the population is given by the following differential equation...

Homework Statement A culture begins with 100,000 bacteria and grows to 125,000 bacteria after 20 min. What is the doubling period to the nearest minute? Homework Equations Current=Original(rate)^time The Attempt at a Solution I can get make the first part out...

I have this delete s275x05.txt; diary s275x05.txt clear; clc; close all; echo on % % Stewart 275/05 % year=[0:1]; % n+1 = year + 50 pop=[728 906]; p=polyfit(year,log(pop),2) plot(year,pop,'o','MarkerFaceColor','r') hold on x=[0:0.01:6]; y=exp(polyval(p,x)); plot(x,y) hold on %part...

Homework Statement http://img14.imageshack.us/img14/1286/99892583.jpg Homework Equations in the pictureThe Attempt at a Solution so i know that p(0)e^2k = 950 p(0)e^8k = 9500 how do i find k? for p(0) i get 440.950939 is that right? btw. ignore the answers in the picture

Homework Statement The population of a country is growing exponentially. The population in millions was 120 in 1970 and 150 in 1980. (a) What is the population t years after 1970? (b) How long does it take the population to double? (c) When will the population be 400 million...

A population grows at a constant relative rate. After 10 months the population grows to 72, and after 18 months the population grows to 96. Find C and k. the answer I got was c=50.25 and k=.0359 can somebody just double check for me? I don't know if the method I was used was correct.

I am trying to model the growth of a population which replicates at a rate of 160% every four hours. Also 50 000 members die every hour. so t denoting time in hours, P denoting the population, k being 0.4 I wrote: dP/dt=kp-50 000 *t Is my approach to solving the differential faulty...

i guess I am trying to find the relationship between population growth and time. bacteria population is 1000 during time 0minutes. bacteria p.: 2000 time: 30 minutes bacteria p.: 4000 time: 60 minutes bacteria p.: 8000 time: 90 minutes bacteria p.:16000 time: 120 minutes...

Malthus' principle of population growth can be written as the differential equation y'=ky where y(t) is the population t years after the initial measurement and k is the growth constant. The solution to this differential equation is given by y(t)=Ae^{kt} where A is the initial...

Can anyone tell me how to calculate population growth. my book doesn't tell me how to do that. is the formula rN=dN/dt

The Problem: Consider a species in which no individuals live beyond 3 years. Divide the population into four age groups labelled by n = 0,1,2 and 3. Assume that only the second and third groups can reproduce. For each group n let bn denote the birthrate and d_n the death rate. Find a matrix A...

i was just wondering abt this thing for a while... the total no. of human beings are increasing over the decades...which means some %ge of the Earth's matter is getting converted in the form of humans...suppose if the population goes on increasing, then theoretically there should be only humans...

The initial mass of a species of fish in a lake is 7 million tonnes. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 2/year. However, commercial fishing removes fish mass at a constant rate of 15 million tonnes per year...

I am quite sure the first approach is to use partial fractions but I am unclear how to finish this equation 1/P*dP/dt=b+aP

Hello I am having major difficulties with two Differential equation. 1. If I have the equation P=2000/(1+9e^.06t). where p=population and t=time. How do I work out when the population is growing the fastest? To work this question out do I just make t the subject and diff twice and let it...

A bacteria culture starts with 300 bacteria and grows at a rate proportional to its size. After 3 hours, there are 9000 bacteria A.) Find an expression for the number of bacteria after t hours. for this part, i got 300*e^{1.133732*t} B.) Find the number of bacteria after 4 hours. well...

The population of the wolves influences the change in population of the mooses. When the population of the wolves increase, the mooses' population also increase. From the population growth formula of the wolves delta N/delta t = rN(K-N)/K which factor affects the population of the mooses...

Alright, my teacher the sadist gave us an assignment over the holidays, and so far, everyone in my class has gotten all but this. The equation is representative of the population growth of fish in a fish pond. p= m / 1+ae to the -kt p is the intial population, m the carrying capacity...

The following question is from a textbook..and I can't seem to solve it. Can someone help. --============================== The population of a midwestern city follows the exponential law. If the population decreased from 900,000 to 800,000 from 1993 to 1995, what will the population be in 1997?