Exponential Growth: bacetria?
920955
You are on the right track.\n\ny(t) = y(0)*exp(k*t)\n\nWe need to find the growth constant, k and y(0).  There are a couple of ways to do this.  The most direct is to write down the equations for the two times you have data for.  This gives you two equations in two unknowns, which can then be solved for.\n\n1000 = y(0)*exp(k*40 min)\n700 = y(0)*exp(k*20 min)\n\nDivide the second equation by the first equation:\n\n700/1000 = exp(k*20 min)/exp(k*40 min)\n0.7 = exp(k*(20-40)) = exp(-k * 20 min)\n-ln(0.7)/20 min = k\nk = 1.78337*10^-2 min^-1\n\nPlug this value back into one of the equations we started with to find y(0):\n\n1000 = y(0)*exp(1.78337*10^-2 min^-1 * 40 min)\n1000 = y(0)*exp(0.71335)\n1000/exp(0.71335) = y(0)\ny(0)= 490\n\nAs a check, we can see if this gives the right result for t = 20 min:\n\ny(20 min) = 490*exp(1.78337*10^-2 min^-1 * 20 min)\n= 490*exp(0.356675)\n= 700 Check!
436245
Growing.\n\nother then that, nothing.
90541
An interesting paper on the subject:\nhttp://www3.interscience.wiley.com/cgi-bin/abstract/108064559/ABSTRACT?CRETRY=1&SRETRY=0
482206
Is exponentially proportionally to the load.
46182
i think it would be f-critical times Degress fredom alpha.  but i am not 100%.  i'm going with that b/c i dont think there is addition in that function.  the real question is how much turkey is there in the turkey test?
353301
See p. 541 of Econometric Foundations by Mittelhammer, Judge and Miller.  Will be a bit tough to explain on Yahoo.  Actually, I don't like this book, but none of my other ones have this.
492336
As X increases, Y also increases.
1107531
The exponential graph does not take into account that eventually a population will reach a point where it has fully exploited its resources.  It rises slowly at first, but then increasingly steeply, because as the population grows, there are more organisms reproducing. However, the rate of reproduction per organism is constant.  If the graph is drawn on semi-log paper, it will be a straight line.\n\nThe S-shaped curve considers that as a population fills its habitat, resources become scarce, and the population can only then grow slowly.   The initial portion is very similar to the exponential curve.\n \nAs the population fills its habitat, the rate of growth declines, until eventually, the population is stable at some maximum, called the carrying capacity.  This is called the stationary phase.\n\nIf populations grow quickly, they can exceed the carrying capacity, degrade the environment and experience swift decline.   After the population crashes, the environment can rebound.  \n\nThis is illustrated in some population of predators versus prey.  Where populations cycle between growth and decline.
806438
The exponential formula for growth would be\n\nn(t) = n(0)* e^(t/tc), where n0 is the initial number of cells, and tc the "time constant" for growth.  This can also be written\n\nn(t)/n(0) = e^(t/tc)\n\nYou are given that when t = 6mo, n(6)/n(0) = 2\n\ntherefore 2 = e^(6/tc);   solve this for tc:\n\nln(2) = 6/tc, and tc  =  6/ln(2) =  8.656\n\nThe equation is now n(t)/n(0) = e^t*/8.656\n\nwhere t is in months.   For t = 3 years, that is 36 months, so n(36)/n(0) = e^(36/8.656) = 64.0   For t = 6 years, or 72 months n(72) = e^(72/8.656) = 4.10*10^3
140255
A graph of many rates (rate of reaction, population growth, etc.) produce exponential curves (asymptotic).\nThese are difficult to interpret.\nTo linearise the curve plot log y against x, or log y against log x. The properties of the rate can now easily be established.\nHave a look here (note, second reference is PDF format):
37851
I quite disagree with Darrius. The law of accelerating returns and Moore's law make it inevitable that by no later than 2040 we will have advanced so far technologically that we will be able to do all that they do in the Matrix movies and more. We won't need  a huge spike driven into a hole in the back of our heads though. (Ever hear of wireless networks?)\n\nWithin a decade or two we will be able to supplement our brains with implants allowing us to parallel process (multi-task), enjoy instant and total memory recall, and communicate via the then ubiquitous, wireless Internet with other people or computers including being able to download information. \n\nThis is just scratching the surface. Check out my source links and hang on, we're all about to go on one heck of a ride.
136373
http://news.uns.purdue.edu/html3month/2006/060203.Lech.regnier.html
163546
Exponential graphs appear EVERYWHERE in the real world. \n\nFor example, they are used in :\n\n1. radioactive dating\n2. acoustic analysis of theatres\n3. stock market management\n4. estimation of stellar magnitudes\n5. analysis of the pH of solutions\n6. analysis of earthquakes\n7. tuning pianos\n8. tempering musical scales\n\nand many many more places.
968183
I'm not really sure what you're asking.  The growth rate would depend on the formula itself, so without the formula, there's no way to determine the answer.  You'd need one to get the other.  I imagine that there could be an infinite number of growth rates and in infinite number of growth-rate-formulas.
98834
The rule of 70 states that to find the doubling time for any exponential growth, divide 70 by the percent of annual increase. So, if the population grows 10% per year, it will double in 7 years.
191015
Since the first 3 answerers didn't really comment on where they got their answers from, I thought a more detailed answer was called for.\n\nThere's a general formula for these types of growth, which also applies to things like radioactive decay rates and interest rates:\n\nP(t) = P(0)*e^(r*t)\n\nP(t) is the population at time t\nP(0) is the population you're starting out with (the population at time 0)\ne is the "natural base" number\nr is the rate of change\nt is the time\n\nIn this case, r is .005 (.5 percent), t is 3 years (878-875), P(0) is 360, and P(t) is our only unknown.  So plug them in:\n\nP(3) = 360*e^(.005*3) = 365.440703...\nWhich rounds to 365.\n\nThe first answerer's method becomes inaccurate after a while; for example, 50 years should be 462, not 450.  The second answerer is better.  The third is just plain wrong, with no explanation of his methods.
1147329
Basic fact of life:  grow or die.