What type of growth or decay function does one encounter in work or in personal life?
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1.  The von Bertalanffy growth function (VBGF) introduced by von Bertalanffy in 1938 predicts the length of a shark as a function of its age, L = L(t): L(t) = Loo - (Loo - Lo) exp(-kt) \n2.  Examples of exponential growth\nBiology. \nMicroorganisms in a culture dish will grow exponentially, at first, after the first microorganism appears (but then logistically until the available food is exhausted, when growth stops). \nA virus (SARS, West Nile, smallpox) of sufficient infectivity (k > 0) will spread exponentially at first, if no artificial immunization is available. Each infected person can infect multiple new people. \nHuman population, if the number of births and deaths per person per year were to remain constant (but also see logistic growth). \nMany responses of living beings to stimuli, including human perception, are logarithmic responses, which are the inverse of exponential responses; the loudness and frequency of sound are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a smooth (linear) increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy of the estimation of differences at high levels of stimulus is much less important for survival. \nElectroengineering \nCharging and discharging of capacitors and changes in current in inductors are also exponential growth and decay phenomena. Engineers use a rule of five time constants to estimate when a steady state has been reached. \nComputer technology \nProcessing power of computers. See also Moore's law and technological singularity (under exponential growth, there are no such singularities). \nInternet traffic growth. \nWikipedia:Modelling Wikipedia's growth - an analysis of Wikipedia's growth rates based on article growth rates and other statistics \nInvestment. The effect of compound interest over many years has a substantial effect on savings and a person's ability to retire. See also rule of 72 \nPhysics \nAtmospheric pressure decreases exponentially with increasing height above sea level, at a rate of about 12% per 1000m. \nNuclear chain reaction (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple neutrons, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the probability of neutron absorption exceeds the probability of neutron escape (a function of the shape and mass of the uranium), k > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction. \nNewton's law of cooling  where T is temperature, t is time, and, A, D, and k > 0 are constants, is an example of exponential decay. \nMulti-level marketing \nExponential increases appear in each level of a starting member's downline as each subsequent member recruits more people.
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Acheiving personal happiness is the primary goal in this life.One is in this world to experience joys and fulfilment.What-ever be the reason,past is dead.Live in the present and dream about your future . Plan actions for  where you would like to be years hence. Keep youself physically and mentally busy.
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Dead stuff doesn't grow. Instead, what is perceived as "growth" is acually the surrounding tissues receding, or shrinking, as a result of moisture loss from the once living surrounding tissue. Hair and nails are mostly protein (keratin) and contain very little moisture (in comparison to skin cells) and thus don't shrink.
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I think the full process of growth terminates at the age of 25, when it get reversed and falls into decay. So, theoretically, I would say it is possible.
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career development keeps you from career plateau.  when you plateau, you no longer achieve higher level thinking, thus development keeps you thinking, getting your masters is an example of career development, or going to seminars, etc... as long as you get involved and build on your career, expand your field within your career, grow with your career, you are developing.  teachers, for example are always trying to be  better teacher, so we hope, so they go to workshops, seminars, career development trips, training to know what's new, what's working, and what's not.  after 30 years of teaching, i know some teachers that are still developing their careers.\nExmpl...computer training, stress reduction, disipline and classroom control, methods, etc...(note: these are career dev. progs for education).
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14 years. Happy most days. But everyone has a bad day, and sometimes life throws you curves. People grow and change daily the key for us is growing together and trying to stay on the same tracks.
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Compound Annual Growth Rate.\nIts a way of expressing the annual growth rate (or rate of increase) of something when taking compounding into account.\nI don't have the forumla handy.  You can use a calculator like an HP 19B Business Consultant II calculator to figure it out.  Or you can use Excel.
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Me!  Making the best of self is a measure of growth.
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Success and happiness are all relative to your point of view, assuming that you are referring to personal success.\n\nGoal Setting\nTypically, you will want to set goals for yourself.  The goals will help you achieve what you want and help you measure your progress.  As you go through life your priorities will change as will your goals.\n\nSee the link below for some more information on goal setting and how it can help you acheive what you define as success.  This site talks about goals for a career.  These same principals can apply just as well for your personal life.
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Application 1 : Exponential Growth - Population\nLet P(t) be a quantity that increases with time t and the rate of increase is proportional to the same quatity P as follows\n\nd P / d t = k P\n\n\nwhere d p / d t is the first derivative of P, k > 0 and t is the time.\n\nThe solution to the above first order differential equation is given by\n\nP(t) = A ek t\n\n\nwhere A is a constant not equal to 0.\n\nIf P = P0 at t = 0, then\n\nP0 = A e0\n\nwhich gives A = P0\n\nThe final form of the solution is given by\n\nP(t) = P0 ek t\n\n\nAssuming P0 is positive and since k is positive, P(t) is an increasing exponential. d P / d t = k P is also called an exponential growth model.\n\nApplication 2 : Exponential Decay - Radioactive Material\nLet M(t) be the amount of a product that decreases with time t and the rate of decrease is proportional to the amount M as follows\n\nd M / d t = - k M\n\n\nwhere d M / d t is the first derivative of M, k > 0 and t is the time.\n\nSolve the above first order differential equation to obtain\n\nM(t) = A e- k t\n\n\nwhere A is non zero constant.\n\nIt we assume that M = M0 at t = 0, then\n\nM0 = A e0\n\nwhich gives A = M0\n\nThe solution may be written as follows\n\nM(t) = M0 e- k t\n\n\nAssuming M0 is positive and since k is positive, M(t) is an decreasing exponential. d M / d t = - k M is also called an exponential decay model.\n\nApplication 3 : Falling Object\nAn object is dropped from a height at time t = 0. If h(t) is the height of the object at time t, a(t) the acceleration and v(t) the velocity. The relationships between a, v and h are as follows:\n\na(t) = dv / dt , v(t) = dh / dt.\n\nFor a falling object, a(t) is constant and is equal to g = -9.8 m/s.\n\nCombining the above differential equations, we can easily deduce the follwoing equation\n\nd 2h / dt 2 = g\n\nIntegrate both sides of the above equation to obtain\n\ndh / dt = g t + v0\n\nIntegrate one more time to obtain\n\nh(t) = (1/2) g t + v0 t + h0\n\nThe above equation describes the height of a falling object, from an initial height h0 at an initial velocity v0, as a function of time.\n\nApplication 4 : Newton's Law of Cooling\nIt is a model that describes, mathematically, the change in temperature of an object in a given environment. The law states that the rate of change (in time) of the temperature is proportional to the difference between the temperature T of the object and the temperature Te of the environment surrounding the object.\n\nd T / d t = - k (T - Te)\n\n\nLet x = T - Te so that dx / dt = dT / dt\n\nUsing the above change of variable, the above differential equation becomes\n\nd x / d t = - k x\n\n\nThe solution to the above differential equation is given by\n\nx = A e - k t\n\nsubstitute x by T - Te\n\nT - Te = A e - k t\n\nAssume that at t = 0 the tempearture T = To\n\nTo - Te = A e 0\n\nwhich gives A = To - Te\n\nThe final expression for T(t) i given by\n\nT(t) = Te + (To - Te)e - k t\n\nThis last expression shows how the tempearture T of the object changes with time.\n\nApplication 5 : RL circuit\nrl circuit for application 5\nLet us consider the RL (resistor R and inductor L) circuit shown above. At t = 0 the switch is closed and current passes through the circuit. Electricty laws state that the voltage across a resistor of resistance R is equal to R i and the voltage across an inductor L is given by L di/dt (i is the current). Another law gives an equation relating all voltages in the above circuit as follows:\n\nL di/dt + Ri = E , where E is a constant voltage.\n\nLet us solve the above differential equation which may be written as follows\n\nL [ di / dt ] / [E - R i] = 1\n\nwhich may be written as\n\n- (L / R) [ - R d i ] / [E - Ri] = dt\n\nIntegrate both sides\n\n- (L / R) ln(E - R i) = t + c , c constant of integration.\n\nFind constant c by setting i = 0 at t = 0 (when switch is closed) which gives\n\nc = (-L / R) ln(E)\n\nSubstitute c in the solution\n\n- (L / R) ln(E - R i) = t + (-L/R) ln (E)\n\nwhic
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Rate of change can be negative, positive and zero; If it is defined. some times it is undefined. In this case it goes to infinity or the function is not continuous or it is a vertical line.
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Age involves the passage of time. If time were at a stand still, everything remains as it is when time stopped. There would be no growth physically, emotionally, spiritually, etc.Time involes changes both good and bad which rounds out life, and makes life worth living. Think about this for a minute,if nothing changes, wouldn't life be unbearable BORING? Think about what I have said here, and truly have a very Happy 30th birthday.
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doing things in detail and w/ persistance.
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Hi, it depends on particular organisms. Check the link below for basic mathematical formulas you may be able to use.\n\nA study is done in which the number of bacteria in a liquid culture is monitored over a period of several hours. Ten observations were made:\n\n\nTwo questions need to be answered:\n\nIs this data consistent with an exponential growth model: N = N0ekt, where \nN0 = the number of bacteria present initially (at t = 0)\nk = a growth rate constant\nN = the number of bacteria present at a given time t,\nand e is the fundamental mathematical constant forming the base for natural logarithms. \nIf the answer to the first question is "yes", then what are the values of N0, k, and t2 (the so-called doubling time) for this bacterial system?\nThe experimental measurements listed above indicate the number of bacteria are growing with time. If we plot the observed values of N (vertically) against the elapsed time, t, in hours, we get a graph (available on web page below).\n\nYou can draw a smooth curve through the experimental points as shown in this figure, and the points all seem to lie relatively close to this curve. Further, this curve looks quite a bit like the graph of an exponential function, but from what we see, it might just as well be part of a parabola or of one of a number of other curves that result when various algebraic forms are graphed. This graph suggests that the answer to the first question may be "yes", but we would usually want stronger evidence than this to draw a definite conclusion. The trouble here is that it is difficult to distinguish precisely and reliably between the curves are the graphs of quite different mathematical functions.\n\nThere is, of course, one curve that is easily recognized by everyone - the straight line! In this situation, the logarithmic function can be used to rewrite the exponential growth formula into a form that will allow us to create a plot that does give a straight line when data is the result of an exponential growth (or decay) process. Start with the exponential growth formula:\n\nN = N0 ekt\n\nSince this involves an exponential with base e, it is "natural" to use natural logarithms - those based on the number e. Using the more common notation ‘ln’ for ‘loge’, we simply take the logarithm of both sides of the previous equation:\n\nln N = ln(N0 ekt)\n\n= ln N0 + ln(ekt)\n\n= ln N0 + kt ln e\n\n= ln N0 + kt\n\nHere, we have used two of the three basic properties of logarithms to manipulate the right-hand side, namely that\n\nlog (AB) = log A + log B \n\nlog (Am) = m log A \n\nFurther, in the last step we took advantage of the fact that by choosing to work with natural logarithms, ln e = logee = 1. Thus, the exponential growth formula can be written in the logarithmic form\n\nln N = kt + ln N0\n\nIf the exponential growth formula is correct and we were to plot ln N along the vertical axis of our graph (rather than N itself), and t along the horizontal axis, then the equation of the plot we are preparing will have the generic form\n\nvertical quantity = constant x horizontal quantity + another constant \n\nBut this is just the equation of a straight line. The plot that results using the data given above is available on web site below.\n\nAlthough the values written on the vertical axis are values of N, this graph is ruled vertically so that the vertical distances are actually proportional to ln N. Since one scale is logarithmic (the vertical one) whereas the other graph scale, the horizontal one, is the ordinary uniform spacing type, this is called a ‘semilogarithmic plot’.\n\nAt any rate, the figure indicates that the points are scattered about a straight line, the scatter due to small random errors in measurement. Since the plot of ln N vs t gives a straight line, we have confirmed that\n\nln N = kt + ln N0 (equation *) \n\nis a valid formula for this data, and therefore, so is its equivalent, N = N0 ekt, valid for this data.
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Law of averages at work. What moves Up has to Come down.\n\nIf only our investors knew this simple truth !!
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(m)\n\nHappiness, ventured William James, the noted 19th century philosopher/psychologist, is reflected in the ratio of one's accomplishments to one's aspirations. This suggests, of course, that when it comes to feeling happy in our lives, we can choose one of two paths: continually add to our list of accomplishments--or lower our expectations.\n\nSince then, researchers have suggested new definitions of happiness and how we should go about getting there. In their attempt to understand and quantify the state of "subjective well-being" (lab-speak for happiness), a new ratio/question has emerged: How many positive vs. negative experiences must people have before they can call themselves genuinely "happy"?\n\nThe general consensus of current research is that happiness is greatest when we combine frequent numbers of good experiences with a few very intense ones. The good experiences may include, for example, having a good, productive job, a caring spouse or romantic partner, and several hobbies or interests that one takes pleasure in. An occasional romantic getaway weekend, the birth of a new child, or garnering recognition for some personal or professional deed would satisfy the need for intense pleasures.\n\nYet, to feel happy, our focus nevertheless needs to be on the frequency, not the intensity, of positive events in our lives. Learning how to take pleasure in the littler victories, recognizing their importance in our lives, and working hard to minimize the negatives will accomplish more than waiting around for a burst of intense pleasure. When we place an overriding emphasis on the "big moments," we run the risk of disillusionment and disappointment--we miss out on the very things that do the scut work of happiness.\n\nWhile there appears to be no one route to happiness, information gathered by researchers from interviews with thousands of subjects of varying ages, economic backgrounds, education level, age, sex, and cultural origin suggests that there are steps we can take to improve our overall satisfaction and well-being. To describe them for you, we sought out four top happiness researchers from across the United States and Canada.\n\nWe asked all of them the same five questions:\n\no How do you define happiness?\n\no What are the best ways to get there?\n\no Who is happy...happier...happiest?\n\no What doesn't lead to happiness (that we mistakenly think will)?\n\no Has the definition of happiness changed significantly over the last few decades?\n\nDrawing on self-report scales, longitudinal studies, and clinical interviews with thousands of subjects, the following experts offer some practical advice on the subtle art of feeling good.
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Personal consumption \nGovernment expenditures \nPrivate investment \nInventory growth \nTrade balance