Growth Definition and 326 Threads

I was wondering how fast x! grows as it approaches infinity as compared to x2, 2x, and xx. The last one was fairly obvious since x*x*x*x... > x(x-1)(x-2)(x-3)... But I can't figure out a way to show that x! grows faster than x2 or 2x. I know it grows faster since I can compare the graphs of...

A rabbit population satisfies the logistic equation dy/dt=2*10^-7y(10^6-y) where t is the time measured in months. The population is suddenly reduced to 40%of its steady state size by myxomatosis. a) If the myxo' then has no effect how large is the population 8 months later? b)How long will it...

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.

Hello, I'm in need of someone to show me how to fit a bacterial growth curve to data in Prism, preferably using the Gompertz function. I also need someone to show me how to assess the goodness of this fit. I have many different growth curves and I need to compare the parameters. Hopefully...

Hello! Excuse me for my very basic understanding of math. I'll try and present my idea and problem clearly. I'd like to devise a payout structure for a tournament. 20% of the entrants will be paid. The payout will be an exponentially sloping function. The payout is in percentages that equal...

Back to how income differences is explained in neoclassical theory, one can ask the question why GDP/capita is $5200 in Morocco and $35 500 in France. Real GDP per capita has grown at a rate of about 3.5% from 2008– 2012, GDP/capita in France grew in the same period at a rate of 1.1%...

Homework Statement dY/dt = y(c - yb) C and B are constants. Im supposed to find and explicit solution for y, but I am having trouble. Homework Equations The Attempt at a Solution dY/y(c - yb) = dt ∫(1/c)dy/y + ∫(b/c)dY/c - yb = ∫dt (i used partial fraction decompositions)...

What is the maximum approximate black hole size that would have negative growth rate as a function of average local mass density (and/or any other relevant parameters)? In other words, when does an evaporating black hole become a growing black hole and vice-versa? Cheers Eric

Hey guys, I'm new here so please be easy on me if I break any "unwritten" rules. I'm doing a design study on brittle crack growth in ductile materials. As I understand it, when a macroscopic crack is found in a load bearing plate, holes can be drilled at each end to reduce the internal...

I'm currently working on a project for a code that does umbrella sampling of a 2-D Ising model [size LxL of a magnet (analyzing up or down spins)]. The next step is to take my code to analyze a nucleation region and its growth by varying the temperature above critical. Before I even attempt to...

This whole chapter has been tripping me. My professor made-up another way of doing this, which I'm having a hard time understanding. He's a really intelligent guy(even other professors say it) so he can do this, but I'm having a hard time understanding his way. I went to tutoring today, they...

Homework Statement Why do waves get larger as they approach a beach? Discuss in terms of wave packets and group velocity. Homework Equations Let h be the height of the water. We can write h(x,t) as: h(x,t) = ∫dk*A(k)*cos(kx-wt), where w = w(k) The Attempt at a Solution What...

Is this question equals to "after 9 hours"? I'm saying this because with each 2 hours, it's growing by a factor of 6 right? So it should normally be "after 9 hours" that the bacteria would have that mass?! I just want to know if it's right or not. I know of another way to solve it but it gives...

1. Let's say that at the end of 2010, the population of Athens was 100,000. Let's also say that the relative growth rate of the population was 2% per year. What's the population at t = 0.5 years after the end of 2010? 2. To solve this sort of problem, I thought I'd have to use: y= A(1+b)t A is...

Hello, I am working through some proofs from the following document: Function Definitions Under Calculation of Big - Oh, some theorems are provided that classify the growth rates of functions in relation to one depending on what the limit is as the input approaches infinity. One proof is...

Much of what people say about the vicinity of black holes doesn't seem to make sense. For instance, it seems to be impossible for a black hole to grow by "ingestion" by scooping up matter around it or in its path, at least in the traditional sense. Gravitational time dilation takes care of...

I am studying for my undergraduate Astrophysics module and the lectures notes say that that all abundances are measured relative, in terms of H = 12.00 by mass or number of atoms. Is this correct? I thought it was all based off of Carbon = 12. Am I missing something?

Homework Statement Before the AP exam Cal Q Luss has 3 hours to cram: during this time, he wants to memorize a set of 60 derivative/integral formulas. According to psychologists, the rate at which a person can memorize a set of facts is proportional to the number of facts remaining to be...

The formula f(t) = I(1 + r)t gives the value of something after it has grown for t years, at rate r, with an initial value I. What if the growth rate r is continuously increasing? What is the formula now? Does it relate somehow to xx?

So, I have a differential equation with growth problem. It is a dm/dt function and I need to get it to dD/dt, change in diameter with time. here is the original functon, dm/dt= (pi/4)(D)^2* (V(D))*(LWC)*E E=1 LWC = 2 V(D) = 343D^0.6 m/s it starts from a diameter of 1mm and grows to...

Hello all! I want to know the difference between growth rate and net growth rate(the context is broad-population or economic,take it as you may).

I'm curious about food preservation. Which are the most common dangerous bacteria? How quickly do they grow? What sort of conditions? And how many must be present to pose a threat to a human? Also, how do they survive the stomach? Do they infect via the mouth or esophagus?

Homework Statement A culture of bacteria have a growth rate (as a percent) given by kb per year, constant k>0 and b is the number of bacteria. A virus removes bacteria at a rate of m bacteria per year. I am trying to model this information using an ODE, but might be making a mistake. Homework...

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 The bacteria in a tuna sandiwch left out of refrigerator grows exponentially. The number of bacteria in a sandwich at any time, t, in minutes can be modeled by the function N(t)= No[3^(t/35)] a)if there are 600 bacteria initially, how long will it take for the bacteria...

Good day, I am a first year in college and I am taking a course in systems biology. For this assignment we are to use the Gompertz growth formula and fit it to a data set of tumor growth, fitting the parameters and graphing everything with mathematica. As of now, I am stuck at the part where I...

I recently came up with a theory that was the product of a 2 hour long thought experiment. Its more of a correlary than a theory I suppose. Please share input but approach it with an open mind and don't form an opinion without giving it a chance. Here it goes. According to Carl H. Flygt, "the...

I'm a very conceptual person, and I've been reading about exponential and logarithmic growth but don't fully have the kind of conceptual grasp on the two and how they differ that I'd like, so I"m curious: What is the difference between exponential growth and logarithmic growth and what causes...

These are not homework questions. I saw these and some other questions mentioned as discussion in a document. I could find answer to others. I need just 3 or 4 sentences simple answers to these so that I can get a head-start. 1. Compare at least two different examples where concentration...

Homework Statement A biomedical company finds that a certain bacteria used for crop insect control will grow exponentially at the rate of 12% per hour. Starting with 1000 bacteria, how many will they have after 10h? Homework Equations Topic is application of differential equations...

Question: find the rate of change of (s) with respect to time(t), is inversely proportional to the square root of (s) Write a differential equation for this statement. Find the general solution to this equation If initially (s)= 100, and after six seconds (s)= 144, what is the value of...

Homework Statement I try to order given functions and I am stuck with evaluating the following: f(n)= (n+1)! and g(n)=n^{logn} Homework Equations \lim_{n\to\infty}\frac{f(n)}{g(n)} = 0 then g(n) is faster growing. \lim_{n\to\infty}\frac{f(n)}{g(n)} = \infty then f(n) is...

If f(x) if big-theta of g(x), is it also always the case then that g(x) is big-theta of f(x)?

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...

I'm trying to figure out the growth rate of a function. Below is what I believe to be the solution, but I'm wondering if I've properly taken into account all the factors necessary, so I wanted to see if this appears correct. $$\Large\frac{3(n+1)^{\frac{2}{3}}}{2}-\frac{3(1)^{\frac{2}{3}}}{2}$$...

Homework Statement A bacteria culture starts with 840 bacteria and grows at a rate proportional to its size. After 3 hours there will be 2520 bacteria. How long will it take for the population to reach 1030 ? 2. The attempt at a solution dP/dt = k*P dP/P = k*dt *Integrated both...

Hey everyone, I'm new here and wanted to see if I've gotten this question right, thanks in advance. 1. Consider a lake that is stocked with walleye pike and the population of pike is governed by the logistic equation: P' = 0.1P(1-P/10) where time is measured in days and P in thousands of...

Homework Statement A doped silicon ingot is to be grown by the Czochralski technique with a dopant concentration of 1016boron atoms/cm3. If k0 = 0.9 for boron/Si, what concentration of boron atoms should be in the melt? Homework Equations Cs/C0 = k0 (1 - m/m0) k0-1 k0 = Cs / Cl The...

As I understand things, a "growth investor" is someone who invests in a brand new, untested company and hopes to get a high return on their investment. Pros: High Payoff "Principle Investment can double?/triple?/exponentiate? if the company succeeds." Cons: High Risk "All money invested in...

Homework Statement Consider the exponential function f(x)= ab^(x) a) Show that (f(x+1))/f(x) = b b)Use the results from part (a) to explain why there is no exponential function of the form f(x)= ab^(x) whose graph passes through the points (0,4) (1,4) (2,8) (3,24) and (4,72)...

I have no idea where this topic belongs since it combines physics and biology. Is there a way to describe life, growth, and evolution in terms of Atoms or Physics. Or are they two completely different things?

Is it normal that my fingernail growth rate is not constant? Mine definitely grow in spurts. I keep them very, very short (about 1 or 2 mm), so it's easy for me to notice how the growth rate changes. About every 3 or 4 months, the rate speeds up dramatically.

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...

Hello community, in project group I am doing some in which I definitely need your help. Basically what I am intending to do is to examine the cell proliferation of cell of the colorectal carcinoma. The data I will receive is from the xCELLigence system and generates so called cell...

The equation I used for these are: If N=Noekt then DN/Dt=N0kekt so the two problems I have trouble with is A radioactive substance has a decay constant (k) of -.0539 per year. If 371 grams of the material is initially present, what is the instaneous rate of change of the substance at times...

Determine the rate of growth in the population of ants for each of the ten days: Day 0 - 65 ants Day 1 - 72 ants Day 2 - 79 ants Day 3 - 87 ants Day 4 - 95 ants Day 5 - 104 ants Day 6 - 114 ants Day 7 - 123 ants Day 8 - 134 ants Day 9 - 146 ants Day 10 - 161 antsI believe to solve this you need...

I went to see an orthopedic specialist this year, when I was 15 years and 5 months old. I am 5 ft, 11 1/4 in. The specialist looked at my then-recent X-rays and I was not even halfway done growing. (I'm pretty sure I scored a 2 out of 5.) I am due for another X-ray sometime next year, at...

Homework Statement City has 500 000 citizens. One citizen knows a gossip. After 10 minutes, he tells that gossip to another 2 citizens. Those 2 citizens tell that gossip to another 2 citizens(both of them tell 2 citizens). After what time whole city will know the gossip? Homework Equations...

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...