what is an exponential gaph and how it is used in really life?
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):
235709
This is a very perceptive question. Well done! You deserve an answer.\n\nWe are the life force, life energy, divine energy,elan vital, (that's french), whatever you want to call it. The energy peculiar to life which acts upon material in the physical universe and animates it, mobilizes it and changes it.\nBut we are suscepable to alteration in character or vibration and can become enturbulated. Hence the mess we sometimes make of the physical universe.\nSo there is a similarity to energy in the physical universe therfore batteries is a great analogy. I like it.
502964
the term "imaginary" merely means that you can't go out and buy 3i gallons of gas.  Mathematically it makes perfect sense to be able to construct a number system that allows the square root of a negative number to exist and to be used.  It also works in electronics and a lot of other engineering applications.
1040642
CHECK THIS OUT:\n\nhttp://www-xl.cingularextras.com/fuel/enduser/portal/endUserHTMLDesc?resourceID=42511&descAction=deepDesc&dc=0
803485
I think it's p=problem, i=infere' g=gather info? t=test e=expirement\n           good luck
388069
This is with a calculator or Excel, right?\n\nYour calculator probably attempts to calculate x^(1/3) by taking the natural log of x:\n\nx^(1/3) = exp(ln(x)*(1/3))\n\nbased on the fact that:\n\nln(a^b) = b * ln(a)\n\nbut you can't take the log of a negative number.  It doesn't recognize the fact that the cube root is well-defined.\n\nYou can help it along by substituting:\n\nsign(x)*(abs(x))^(1/3) = x ^ (1/3)\n\nbasically taking the sign out at the beginning and putting it back at the end.
526116
Basically, all you need to know is the initial amount (8.0 grams I assume), and the half life (46 days).  Then you can build an exponential model of the form:\n\nA(t)=A*e^(k*t)  \nA is initial amount\nk is decay constant\nt is time\n\nKnowing that after 46 days, there will be half as much present:\n\n4=8*e^(k*46)\n\nThen solve for k using logarithms.  \n\nln(0.5)=46k\nk=ln(0.5)/46=-0.01507\n\nSubstitute into equation to get time dependent equation:\n\nA(t)=8*e^(-0.01507*t)\n\nNow you want to know how much is left after t=184:\n\nA(184)=8*e^(-0.01507*184)\n\nA(184)=0.5 [grams]\n\nViola....
95797
Like fLoWeRs said....you didn't give the equation! So I'm going to ansswer you based on what I regard as a standard exponential.\n\nf(x) = ae^bx + c\n\nThis is a fairly standard exponential as far as I know, and there's no reason why "b" can't be negative. In fact, if it weren't in some cases, we'd be living in a pretty funky place.
338108
A Natural log. It is expressed as: ln()\nFor example: ln(e^2) = 2
1156569
The problem is not that you can't take the log of a complex number. The problem is that log is multiple valued in the complex plane. In other words, the exponential function is not one-to-one. You can take the 'principle branch' of the logarithm, but then you can lose certain of the rules of logarithms.\n\nThe upshot is that when you take the log of -1, you either get an infinite set of values (.., -pi*i,  pi*i, ...) and another infinite set of possibilities for the log of 1 OR you lose the property that log(a^b)=b*log(a) that you used in your first paradox. This is just a fact of life when working with complex numbers. In the second, BOTH -pi*i and pi*i are logarithms of -1, so the argument fails. It's somewhat like saying that the squares of -1 and 1 are the same, so -1=1.
599454
Survival of what exactly?\n\nYou could try an exponential  N=A*exp(-Bt) as used for radioactive decays, with N the nu,ber of survivors.\n\nA logistic function if the numbers of deaths show a normal distribution in time, like for car spare parts.\n\nhttp://en.wikipedia.org/wiki/Logistic_distribution
85527
I "Googled" for it but couldn't find where anyone had actually written it all out and posted it.  This seems to come close:\n\nAN ALGEBRAIC EQUATION FOR THE HALTING PROBABILITY\nhttp://www.cs.auckland.ac.nz/CDMTCS/chaitin/berlin.pdf\n\n"The result is an exponential Diophantine equation with the parameter n and the property that it has infinitely many solutions if and only if the nth bit of Ω is a 1."\n\n"It takes the compiler only a few minutes to convert the 300-line Lisp interpreter into a 200-page 17,000-variable universal exponential Diophantine equation."
356040
elementary mode analysis Is also known as extreem path way analysis. It defines the limiting bondaries of the operation of a metabolic network. The normal approach is to use singular value decomposition to determine the constraints of a metabolic network.\n\nTo be honest its a bit over rated since all it does is define the feasable space of operation of a cell. You have to use other principles such as cyberbnetics (maximise growth rate and then use linear programming) or kinetic modeling to determine the expected operation of a cell. \n\nTry a search for Palson - but dont cite or talk to him because he is an arrogant self promoting w****r who doesnt cite competing groups work.
1086154
The reason we call ln(x) "natural" is twofold: first, expressions in which the unknown variable appears as the exponent of e occur much more often than exponents of 10 (because of the "natural" properties of the exponential function which allow it to describe growth and decay behaviors), and second, because the natural logarithm can be defined quite easily using a simple integral or Taylor series--which is not true of other logarithms.
187414
2^y = 64/y\n\n\nthis is the intersection of two curves:\nt=2^y\nand\nt=64/y\n\nthat is an exponential and an equilateral hyperbola.\nPlotting the graphs you can have an idea of the intersection (in this case you have the exact solution by plotting integer values, but in general you may need to solve by iterative numeric formulas, after finding graphically a rough estimate of the solution)
787465
Write out the exponentials and use the series for e^x. Other than that, do your own homework.
26116
Exponential functions are used in the everyday lives of people who model (represent mathematically):\n\na) exponential growth - such as the change in a population over time.\n\nb) exponential decay - such as the change in radioactivity of a substance over time.