Growth Definition and 327 Threads

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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.

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...

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?

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...

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...

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...

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...

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...

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...

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)...

[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 ?

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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.

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 -...

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...