Growth Definition and 326 Threads

Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy over time. Statisticians conventionally measure such growth as the percent rate of increase in real gross domestic product, or real GDP.Growth is usually calculated in real terms – i.e., inflation-adjusted terms – to eliminate the distorting effect of inflation on the prices of goods produced. Measurement of economic growth uses national income accounting. Since economic growth is measured as the annual percent change of gross domestic product (GDP), it has all the advantages and drawbacks of that measure. The economic growth-rates of countries are commonly compared using the ratio of the GDP to population (per-capita income).The "rate of economic growth" refers to the geometric annual rate of growth in GDP between the first and the last year over a period of time. This growth rate represents the trend in the average level of GDP over the period, and ignores any fluctuations in the GDP around this trend.
Economists refer to an increase in economic growth caused by more efficient use of inputs (increased productivity of labor, of physical capital, of energy or of materials) as intensive growth. In contrast, GDP growth caused only by increases in the amount of inputs available for use (increased population, for example, or new territory) counts as extensive growth.Development of new goods and services also generates economic growth. As it so happens, in the U.S. about 60% of consumer spending in 2013 went on goods and services that did not exist in 1869.

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  1. T

    Growth rate of integer power sum

    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!
  2. T

    Population growth using logarithims

    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...
  3. russ_watters

    Energy Usage Growth - History and Future

    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...
  4. Jonnyb42

    Why Are Exponential Growth Equations Different?

    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 =...
  5. I

    Solving the Equation for Bacterial Growth in Experimentation

    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...
  6. D

    Continuous Function Outgrowing Polynomial but Not Exponential

    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?
  7. X

    Predicting Population Growth in 1900 with Stewart 275/05

    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...
  8. M

    Bacteria Growth without integration

    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...
  9. H

    How Do You Calculate the Relative Growth Rate of E. coli in a Nutrient Broth?

    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...
  10. S

    What is the Growth Rate Constant for Population Growth?

    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
  11. A

    Why does BLS predict a rapid demand growth for Software Engineers?

    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?
  12. N

    How can Kirchoff's first law be applied to electrical circuits?

    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...
  13. K

    What is the doubling time for bacteria growth in an exponential model?

    I feel like I'm doing everything correctly but my answer for (b) doesn't make any sense. Assume that bacteria in aculture grows according to an exponential growth model. If the number of bacteria grows from 50 to 1000 in 12 hours: a)How many bacteria will be present after 18 hours? b)How...
  14. T

    What is the accurate growth rate formula for a given set of X and Y coordinates?

    Homework Statement Hey, been having a lot of hmwk troubles. I haven't really been taught logistic functions or things relating to the matter. I need to figure out an accurate growth rate formula, and to me it seems to be like an exponential. Note: this is like a table of X and Y coordinates...
  15. K

    Calculte growth is some direction question

    i know that the maximal growth is the gradiend of a function. the formula is: \triangledown f=f_x'\vec{i}+f_y'\vec{j}+f_z'\vec{k} so when i am given a function f(x,y,2x^2+y^2)=3x-5y i am was told that it growth on point M(1,2,6) in direction...
  16. P

    Why Are Facultative Anaerobes Growing at the Water/Oil Interface?

    A facultative anaerobe is growing photoheterotrophically in sterile water, covered with a thick layer of oil inside a test-tube containing 1g fructose. It has been observed that the bacteria are growing at the water/oil interface, and appear to be growing inside the oil layer. Which of these...
  17. D

    Quick question about asymptotic growth

    (\lg n)!\in\mathcal{O}((\lg n)^{\lg n}) right?
  18. R

    How Do You Calculate Compound Interest for Investment Growth?

    Homework Statement An investment pays 8% interest, compounded annually. a) Write an equation that expresses the amount, A, of the investment as a function of time, t, in years. b) Determine how long it will take for this investment to 1. Double in value, and 2. Triple in value. c) Determine...
  19. R

    Exponential growth problem (at least I think it is)

    Homework Statement The measure of effectiveness of a sleep deprived student studying for a test on a scale of 0 to 1 is given by the formula M(t) = ln(t^2) / 3t, where 't' is the time in hours that a student spends studying, 0 < t ≤ 4. Determine the maximum measure of effectiveness of...
  20. L

    A way to organize functions by their speed of growth ?

    A way to organize functions by their "speed of growth"? How does one say formally in math that a certain function grows "faster" than another? Doens't really work for trig functions, i know. you knotice that the exponential function is the function dividing d/dx slower than itself and d/dx...
  21. P

    Exponential Growth for Pre-Calculus

    Hi everyone. My final is coming up for Precalc, and I'm studying my butt off. I was really needing help with this Exponential Growth Equation to find variable t. 8.0e^(.033t) = 59.8e^(.001t) (8 times e to the .033t equals 59.8 times e to the .001t) I would greatly appreciate this...
  22. E

    Growth of a population of wolves

    Homework Statement A population of wolves grows according to the function N(t)=(10N0)/(1+9e^(-t/4)), where t is in years and N0 is the initial amount. How long from t=0 will the population take to double? Homework Equations Refer to below heading. The Attempt at a Solution Not...
  23. J

    Exponential Population Growth: 1970-1980

    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...
  24. R

    Discover the Constant Relative Rate of Population Growth: C=50.25 and k=0.0359

    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.
  25. S

    Understanding Self-Induction: Calculating Current Growth Rate

    This question is about the self induction: The resistance of a coil is 15 ohm, itself induction is 0.6 Henry, it is connected to a source of direct current which gives 120 volts. Calculate the rate of growth of the current at the moment when the current reaches 80 % of its maximum value...
  26. I

    Exponential Growth: Determine t When k=q

    Homework Statement Determine the period in which y = Cekt changes by a factor of q. I have no idea what it is asking.. find t when k=q?
  27. O

    DE equation modeling growth off a tan function

    Homework Statement Data suggests rate of growth of bacteria is proportional to the tangent function evaluated on the amount of bacteria present at time t, up to 1.5 mg. After 1.5 mg, value maintained. pi/6 to pi/3 mg growth in 1 hour. How would I write a DE equation based on this? I'm not...
  28. baywax

    Is Economic Growth Necessary for a healthy economy?

    Is "Economic Growth" Necessary for a healthy economy?? I've asked a few of the number crunchers I've met if economic growth was necessary for a healthy economy and they can't answer me. I've pointed out that unchecked growth inevitably leads to the destruction of a system as is the case with...
  29. L

    Very Simple exponential growth problem

    1. It is estimated that x years from now the value of an acre of farmland will be increasing at the rate of \frac{0.4x^3}{sqrt(0.2x^4+8000)} dollars per year. If the land is worth 500 per acre, how much will it be worth in 10 years? 2. Use integral Since the the function of money...
  30. SdogV

    Motion & Growth: Exploring Photon-Electron Transitions

    So, now I look at a peculiar situation with light photon motion and growth.. Can anyone comment on this thought? Assume frequency is VERY important. Then, E=Mc^2 might imply E- M A'cf where (a) A' is meters squared per sec, i.e., m^2/t (lower case m is meters!) and (b) f is frequency...
  31. K

    Does et^2 Satisfy the Growth Restriction for Laplace Transform?

    Homework Statement The condition to be satisfied for a Laplace transform is U(t)<Mekt Homework Equations I am trying to proove that et2 does not satisfy this The Attempt at a Solution It was suggested that we try taking logarithms of both side: t2<ln(Mekt) t2<lnM+lnekt t2<lnM+kt...
  32. N

    Differential equation for exponential growth

    Homework Statement Viruses are reproducing exponentially, while the body eliminates the viruses. The elimination rate is constant, 50000 per hour. I decided to take down on the minute level, so it would be 50000/60. Pinitial is 10^6 k is ln(1,6)/240, since the growth rate is 160% in 4...
  33. N

    Exponential growth with an elimination rate

    Homework Statement Viruses are reproducing with rate of k ,in t minutes, the function is: f(x) = Po x e^(kt) However there is an elimination rate of a viruses per minute. Homework Equations The Attempt at a Solution We can't say that the new function will be: f(x) = Po x e^(kt)...
  34. C

    General question about growth function?

    [RESOLVED]General question about growth function? P=P0ekt I'm given that a population doubles in number in 4 hours. Does that mean the k in the function equals 0.5 per hour or should I find k from 2=e4*k ?
  35. C

    Solving Population Growth Diff Eq: Is My Approach Faulty?

    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...
  36. S

    Calculate Bacteria Growth Rate: Doubling Time

    Homework Statement A beaker contained 2000 bacteira. one hour later the beaker contained 2500 bacteria. What is the doubling time of the bacteria? Homework Equations rate = (distance)/(time) Time to double = .693/((ln(1+r))^t) The Attempt at a Solution rate = 2500/2000 My...
  37. M

    How Does Bacterial Population Change Over Time?

    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...
  38. S

    Solve Growth Rate Problem: Find Bacteria at Time t

    The problem states that the number of bacteria in a culture is proportional to the number present. The culture has 10,000 bacteria initially, 20,000 at time t1 minutes, and 100,000 bacteria at time (t1+10) minutes. I am asked to find the number of bacteria at time t in terms of t only. The...
  39. B

    Can the mass of a planet or any object affect the growth of a living thing?

    Would there be subtle differences or large differences on how a human or any other living creature grows up from childhood to adulthood into old age if that person were raised on a planet like Earth vs. a place like Jupiter or the moon? In other words , would the transitions from childhood to...
  40. T

    Is .999999... actually equal to 1?

    hey folks, been a long time since i been here, stranded on a tropical island for a few years.. nice to be back to the business. I have a problem with some " rhetoric" i was reading today in one of the old posts. Seems to me that you all seem to think that .999 followed by about 1billion...
  41. C

    Procerin - agents that engender hair growth

    im browsing through products that potentially reverse the cessation of hair growth on one's head. that which I am observing is as follows: procerin ingredients: approximated daily value Saw Palmetto Berries 1500mg ** Zinc...
  42. D

    How Do You Solve and Apply the Logistic Growth Model?

    Given logistics growth model dp/dt=kp(1-p/N) p=population t=time k=unknown growth coefficient (constant) N=unknown carrying capacity (constant) 1) Solve for p explicitly 2) Given collected population data for a given state approximate N and k for that state. This is what I did...
  43. N

    Why Are Calculations of Growth in Salmon Smolt Showing Different Results?

    urgent. Growth in salmon smolt Homework Statement smolt weith is 35g we shall find the weight after 61 days. Homework Equations specific growth rate:; K' = Ln (N2 / N1) / (t2 - t1) growth rate is 1,9 % The Attempt at a Solution I find 110g when I use this forumula...
  44. D

    Differential equations- Pop Growth

    dy/dt=(.5+sint)y/5 what is time t when the population has doubled?
  45. E

    Medical How do our cells know when and how to stop growing and shaping our bodies?

    I want to know how our genes limits and define our growth, I mean, how the osteoblastos knows that they must stop or continue, how our cells knows when to stop growing or dividing, etc. Every human has a unique "morphology", the bones and skull has their own and particulary morphology, but...
  46. K

    Limit of Crystal Growth Furnace

    Homework Statement A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the...
  47. H

    Exponential Growth: Cool Lecture & How to Calculate Doubling Time

    Cool lecture on exponential growth http://sciencehack.com/videos/view/F-QA2rkpBSY The video shows how to calculate the doubling time by dividing 70 by the growth rate. So for a 7% growth rate, the doubling time is 10 years.
  48. K

    Managing Plant Growth: Slowing Down or Stopping Growth with Chemicals?

    I have this headge of a few shurbs/tress growing around my home. However this headge is now infringing on my view over a beautiful hillside and I don't want to remove them because they really compliment the surrounding area. I can't cut them because they are reasonably tall and grow on a slope -...
  49. I

    Exponential Growth Homework: Find y, k, and When Population Reaches 10K

    Homework Statement A bacteria culture starts with 1000 bacteria and grows to a population of 7000 after an hour. a) Find the size of the population after t hours. b) Find the size of the population after 3 hours. c) Find the rate of growth of the population after 3 hours. d) When will...
  50. M

    Nail Growth Hormone: How to Grow Stronger & Faster Nails

    Nail growth hormone? Hello Don't actually know if this is the correct section but anyway. Does anybody know how our fingernails grow? What stimulates them to grow? Is there something i could do more/take to help my nails grown quicker and stronger? Thanks _Muddy_
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