Growth Definition and 312 Threads

Why do economies need to grow? If a country has a narrow social inequality, a high GDP/capita, why does that country's economy need to keep growing? And isn't that insustentable? Do we have the resources necessary to keep increasing the production of goods every year?

Are the two following hypothetical observations contradictory according to GR? 1. Particles fall towards a black hole but never cross the event horizon 2. After observing this for a few million years, the mass of the black hole is observed to have grown over that few million years. Or...

Homework Statement In 1996 the total energy used in the world was 400 million terajoules = 400 exajoules (EJ)= 4 x 10^20J . Projections for energy use vary, but generally it is expected that between 20 and 30TW will be needed by 2025. (a) What percentage growth in energy consumption on an...

So I recently took a job in R&D right out of my Master's program (in electrical engineering). When I was interviewing at the company, I quickly realized that everyone was "Dr. so-and-so". I actually did not interview with a single person that did not have a PhD out of 8 people (except for the...

Homework Statement Water is pumped into a tank. Volume V, is kept constant by continuos flow. The amount of salt S, depends on the amount of water that ahs been pumped in, call it X. ds/dx = -S/V Find the amount of water needed to eliminate 50% of the salt. Take v AS 10,000 gallons...

I am curious to what extent black hole growth can be used to probe understanding of various particles/fields. 1] Dark matter: Let's consider dark matter to be so weakly interacting we can model it as a perfectly non-interacting gas. For even more simplification, let's assume dark matter...

Hi! I am amateur in mathemathicals growth models but I am doing my graduated work in adjust five differents models in some growth parameters in onion, [PLAIN]http://img820.imageshack.us/img820/2929/models.png So my doubt is basically in a derivate for gauss model, i can't derivate this model...

Hi, this contracted company that I am working with has this data. Basically they collect the number of transactions each day. Then they graph these transactions out by Week, always monday - sunday. The data is then stored in a table where the x-axis is the date of the monday the week started...

This topic emerged in another thread but I find it interesting enough to warrant a new thread of its own. The premise is that GDP growth provides more money for investment, consumption, and other spending. To the extent that this extra money allows fiscal discipline to relax, it can have the...

Homework Statement Leaking oil is forming a circular patch on the surface of the sea. The area of the patch is increasing at a rate of 250 square metres per hour. Find the rate at which the radius of the patch is increasing at the instant when the area of the patch is 1900 square metres...

Hi, I am trying to understand how one can derive the lattice growth formula of L (n) = n^2 ( n + 1)^2 / 4 I looked at 2x2 and 3x3 matrices and could count the squares and rectangles in the figure. L (2) = 9, L (3) =36 and so on. However, I am more interested in finding out...

Why is the emf induced in an inductor much larger when the switch connecting it to a battery is closed than when the switch is opened? Somewhere in a text I had read that di/dt is very large when an LR circuit breaks but then its value for growth and decay in an LR circuit is...

Homework Statement A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000. How many bacteria were present initially? Homework...

hi, I am confused about how the vapor pressure affects the materials growth. Can someone comment on the following : If the vapor pressure of a precursor, let's say N, is high then it will be hard to grow a material containing N because it will be hard to incorporate it onto the substrate...

Homework Statement If there is a quantity T comprised of two other quantities such that T=L+B, and quantity T and B are both increasing in every period at a fixed percent such that %growth T > %growth B, it will be true that %growth L > %growth T. It will also be true that as n approaches...

My group is doing a research project for our technical writing class :/ We are studying carbon nanotube production, and are going to say super growth CVD would be the best production method for this company. Would super growth CVD produce usable nanotubes for electrical circuits, batteries, and...

I have a project in my grade 11 biology class to design a controlled experiment showing how some factor affects plant growth, specifically radishes. I have decided to add urea as a nitrogen fertilizer to one group and do nothing to the other leaving all other factors the same between the two...

Hello I am currently researching on crystals and how their growth rate is affected by magnetic fields for my upcoming lab. Most of the information is based on labs but I quite don't understand what they speak of. So I was wondering if anyone here has any nice reading material on crystals and...

Hi I was just wondering if anyone could please tell me what Australians desired trade balance growth rate is Per year of GDP (macroeconomic policies)? is trade aimed at a target of 3 % of GDP? i know inflation = 2-3% GDP = 3% but cannot find trade? Any help would be really...

Homework Statement A Czochralski growth process is begun by inserting 1000 moles of pure silicon and 0.01 mole of pure arsenic in a crucible. For this boule, the maximum permissible doping concentration is 1018 cm-3. What fraction (X) of the boule is usable? (k=0.3) Homework Equations...

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...

Say we take a carrot... or steak (or whatever food you fancy) and put it in a sealed container along with a culture of 'normal' bacteria (I'm talking about the regular bacteria that would be present to decompose food). Now, here comes the question: What would be the most effective way to stop...

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...

Can someone please describe the different growth strategies that plants use in dark and light, and explain why these are important at different stages of growth in natural environments.

I've had some arguments after I assumed ( perhaps wrongly) that electric fields were responsible for the direction that branches grow in. In any case my inquires on this all result in the same answers. That the direction of growth is determined by light and gravity. Do all you agree with...

Homework Statement Homework Equations The mark scheme is 2, 2, 3, 3 For a) ii), it's a sequence of integers up to the floor of n2/2 The Attempt at a Solution We haven't done growth rates of sequences, only of equations. a) i) looks like the growth rate would be 5n, but I...

Sorry if this is the wrong section (already posted it in the biology forum and got no response) but this question comes from a convo I had with some friends the other night.. Say you were able to grow a full size tree indoors (assuming you had the space, nessesary lighting, soil, etc..) and...

Hello, for continuous compouding (in the exponential growth and decay) the function for interest after t years is: A(t) = A0*e^rt A0 should be read A at time 0 in the book, they say when you differentiate this function this is what you get dA/dt = r*A0*e^rt = rA(t) I don't see...

What do you put in diary if you write one, how often you write and where do you store it? I have been using a personal (private) google blogger for past 2 years where I am writing how I am growing and overcoming my weaknesses.

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 As long as N isn't too small, the growth of cancerous tumors can be modeled by the Gompertz equation, dN/dt=-rN*ln(N/K), where N(t) is proportional to the number of cells in the tumor, and r, K > 0 are parameters. (a) Sketch the graph f(N)=-rn*ln(N/k) verses N...

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...

let be the integral equation h(x)= \int_{0}^{\infty} \frac{dy}{y}K(y/x)f(y) here the kernel is always a positive , then if h(x)=O(x^{a}) and the integral \int_{0}^{\infty} \frac{dy}{y}K(y)y^{a} exists and is a positive real number then also f(x)= O(x^{a})

Homework Statement To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the number of units x ordered. The discount decreases the price at a rate of $0.01 per unit ordered. The price per unit for a...

Catastrophic event" stopped growth of galaxy{ON News} Growth of the galaxy stopped,it exploded does this may effect our galaxy http://uk.news.yahoo.com/4/20100311/twl-catastrophic-event-stopped-growth-of-41f21e0.html

dS/dt = kS - W How do I solve this problem if k is the growth constant and W is also constant? Here is what I have so far, but I don't think its quite right: dS/dt = kS - W (kS - W)-1dS = 1dt 1/k*ln(kS - W) = t + C ln(kS - W) = kt + C1 kS - W = C2ekt S = (C2ekt + W) / k...

Homework Statement A cell of some bacteria divides into two cells every 40 minutes. The initial population is 2 bacteria. a)Find the size of the population after t hours b) Find the size of the population after 6 hours. c) When will the population reach 12? Homework Equations...

Homework Statement Hi, can anyone help me solve a differential equation for the logistic growth model? Homework Equations It reads: M'(t) = M(S-M) + I, where M(t) represents the growth of a biomass. "I" represents immigration (in a coral reef) and there is no breeding...

I need to show that \sum_{i=0}^n i^k=\Theta(n^{k+1}) Or equivalently \lim_{n\to\infty}\frac{\sum_{i=0}^n i^k}{n^{k+1}}=CI simply don't know what to do with the sum here. I know that I can rewrite or expand it, but that doesn't seem to help me. Any suggestions? Thank you!

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've put a bunch of effort on this forum into discussing what I consider one of the most important issues facing the US and mankind in general: where to get/how to use energy. I'd like to discuss the history of and projections for future energy use. Here's an article with some charts...

I am learning calculus from a book of mine, and it gave an example problem of exponential growth (as derived from the exponential differential equation of dy/dx = ky to be y=Ce^kt) saying a population is growing at a rate of 2% per year, and says that K, the growth constant, in this case is k =...

Homework Statement The growth of bacteria is proportional to the number present but is being reduced at a constant rate for experimentation. Find the equation for N Homework Equations d(N)/dt = KN-R , N = number of bacteria, K = proportionality const., R = reduction rate. The...

Does there exist a continuous function which outgrows polynomial growth, but not exponential growth? I.e. does a there exist a continuous function f such that \frac{x^n}{f(x)} \to 0 and \frac{f(x)}{a^x} \to 0 for all positive real n and a?

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...

A bacteria culture initially contains P(o) cells and grows at the rate dP/dt = kP where k is a growth constant. After an hour the population has doubled. (a) Determine an expression for the number of bacteria present after t hours. (b) Computer the number of bacteria present, and the rate of...

Homework Statement - A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 63 cells. - (a) Find the relative growth rate. Homework...

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

Why does BLS predict a rapid demand growth for Software Engineers?? in comparison to all engineers in general... http://www.bls.gov/oco/ocos267.htm BLS = Bureau of Labor Statistics (US Govt) And on second thought, will the majority of these jobs be going to foreign workers?

According to Kirchoff's first law for electrical circuits V=RI+L(dI/dt) where constants V, R and L denote the electromotive force, the resistance, and the inductance, respectively, and I denotes the current at time t. If the electromotive force is terminated at time t=0 and if the current is...