What is Growth rate: Definition and 29 Discussions

Relative growth rate (RGR) is growth rate relative to size. It is also called the exponential growth rate, or the continuous growth rate.

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  1. S

    A Physical significance of growth rate in plasma

    Let us say that we have a dispersion relation curve and associated instability curve as shown below for a magnetised plasma, which have been formulated through kinetic theory. The frequencies and growth rate have been normalized w.r.t. cyclotron frequency of proton. My question is: what does...
  2. O

    MHB Calculus I - Relative Growth Rate help

    Here is a picture of the problem: I am firmly stuck on part b). I know that relative growth rate is defined at f'(x)/f(x), but I cannot seem to come up with the right answer. I've tried everything I could conceivably think of. I do not understand why my answer is incorrect, unless I'm...
  3. M

    Show that ##\lim_{n\to\infty}(1+\frac{r}{n})^n=e^r##

    Homework Statement The constant ##e## can be defined in many ways. My first exposure to this number involved compound interests. Specifically, if you decide to continuously compound 1$ at a 100% interest rate for a certain period of time(year, month, etc), you'll end up with ##e##$ where it is...
  4. S

    MHB Gradients of curves to find average growth rate between two points

    Hello Maths Help Board Users, I was hoping for some guidance on the following problem. Thanks in advance for your contributions and time. "A fish population grew according to the following quadratic model - the number of fish on day t is given by P (t) = 800t - t2" Q) Find the average growth...
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    B Logarithmic growth vs exponential growth

    From the book Calculus made easy: "This process of growing proportionately, at every instant, to the magnitude at that instant, some people call a logarithmic rate of growing." From Wikipedia: "Exponential growth is feasible when the growth rate of the value of a mathematical function is...
  6. M

    MHB What is the growth rate of a differentiable function?

    Hey! :o We have that the differentiable function $u(t)$ is stricly positiv for all $t\in [0,\infty)$ and that $w$ is the continuous growth rate of $u(t)$. I want to show that $$w_u(t)=\frac{d(\ln u(t))}{dt}$$How is the formula for the growth rate? Is it maybe given by...
  7. Battlemage!

    I Lim f(x)/g(x) as x->∞ and relative growth rate of functions

    Everyone "knows" that \lim_{x\rightarrow ∞}\frac{2^x}{x^2} = ∞. We "know" this because 2x grows faster than x2. I use quotes because this is just what we're told in basic calculus classes. But what about a theorem for this? I've searched through google, looked through various university homework...
  8. A

    Logarithmic scale for the Laser Intensity.

    I drawed a relation between the growth rate of the material to the laser intensity. After drawing, My professor told me that I must convert both values of the growth rate and the laser intensity to their values in the logarithmic scale. I don't know how. May I get a help.
  9. A

    MHB Calculating Logistic Growth Rate

    I have a logistic growth problem. I know this because there is an upper limit of approximately 21,000 people. I need to calculate growth rate. Would it be something as simple as taking two populations and dividing them to get the rate (X2-X1/X1) to obtain it or is there an equation I am missing...
  10. L

    Optimization growth rate Question

    First post on these forums, thanks all for your help! Homework Statement It is estimated that the growth rate of the fin whale population (per year) is rx(1 - x/K), where r = 0.08 is the intrinsic growth rate, K = 400,000 is the maximum sustainable population, and x is the current population...
  11. J

    MHB Sand Pile Growth Rate: 10 Seconds After Falling

    Sand falls on to horizontal ground at the rate of 9m^3 per minute and forms a heap in the shape of a right circular cone with vertical angle 60^{\circ}. Show that 10 seconds after the sand begins to fall, the rate at which the radius of the base of the pile is increasing is...
  12. marcus

    Concordance value of Hubble growth rate (2014)

    There has been a flood of new data. Cosmologists have not yet settled on a new agreed value of H0. This may help lead to one. http://arxiv.org/abs/1406.1718 The 1% Concordance Hubble Constant C. L. Bennett (1), D. Larson (1), J. L. Weiland (1), G. Hinshaw (2) ((1) Johns Hopkins University, (2)...
  13. T

    Logistic models and the intrinsic growth rate

    In models of exponential growth, we have an intrinsic growth rate (r) that is calculated as the difference of birth rates to death rates. With the logistic growth model, we also have an intrinsic growth rate (r). How then do birth rates and death rates relate to the intrinsic growth rate in...
  14. marellasunny

    Difference between growth rate and net growth rate

    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).
  15. D

    Order by asymptotic growth rate

    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...
  16. D

    MHB Determining the growth rate of a function

    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. $$\Large\frac{3(n+1)^{\frac{2}{3}}}{2}-\frac{3(1)^{\frac{2}{3}}}{2}$$...
  17. P

    DiffyQ Word problem (growth rate)

    I have been trying to figure this problem out for more then 90 minutes and I think I'm past the point where I'm being productive: A population P satisfies the differential equation: P^'(t)=10^{-5}P(t)(15000-P(t)) For what value P(0) of the initial population is the initial growth rate P'(0)...
  18. lisab

    Medical Understanding Fingernail Growth: Is a Variable Growth Rate Normal?

    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.
  19. D

    Averaging Transaction Data for Accurate Growth Rate Calculations

    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...
  20. W

    The effect of a magnetic field on the growth rate of crystals

    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...
  21. M

    What is Australia's desired trade growth rate in relation to GDP?

    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...
  22. 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!
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. H

    Solving Bacterial Population Growth: A Math Problem

    If all I have given is that 1. Bacteria grows at a rate proportional to it's size. 2. It doubles in 2 days. 3. At 10 days, population is 1000. I'm not given the initial bacteria count, I need help setting up the equation. I did: dy/dt = ky => dy/y = kdt => lny= kt + c =>...
  28. B

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

    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 90 cells. the question asks to find the relative growth rate, if we measure t in...
  29. V

    What is the formula for converting monthly growth rate to annual growth rate?

    Hello, my problem is: Let Q(t) = 8(0.87)^t Find the annual and daily growth rate. Can anyone tell me how to set this up? I don't want you to show me the whole problem, just the 1st step. Thanks a ton!