Read about exponential function | 11 Discussions | Page 1

  1. TachyonLord

    I Where does the exponential function come from in roots?

    For example, in linear differential equations, there might be these questions where we'd directly use e∫pdx as the integrating factor and then substitute it in this really cliche formula but I never really understood where it came from. Help ?
  2. E

    I Probability density of an exponential probability function

    I have a model where the probability is spherically symmetric and follows an exponential law. Now I need the probability density function of this model. The problem is the singularity at the origin. How can I handle this? P(r) = ∫p(r) dr = exp(-μr) p(r) = dP(r)/(4πr²dr) One way I tried to...
  3. Peter Alexander

    Fourier transform of exponential function

    1. The problem statement, all variables, and given/known data Task begins by giving sample function and a corresponding Fourier transform $$f(t) = e^{-t^2 / 2} \quad \Longleftrightarrow \quad F(\omega) = \sqrt{2 \pi} e^{-\omega^2 / 2}$$ and then asks to find the Fourier transform of $$f_a(t) =...
  4. TheSodesa

    How to Fourier-transform e^(-2|t|)?

    Homework Statement Determine the Fourier-transfroms of the functions \begin{equation*} a) f : f(t) = H(t+3) - H(t-3) \text{ and } g : g(t) = \cos(5t) f(t) \end{equation*} and \begin{equation*} b) f : f(t) = e^{-2|t|} \text{ and } g : g(t) = \cos(3t) f(t) \end{equation*} Homework Equations...
  5. ATY

    I Lyapunov Exponent

    Hey guys, I need your help. I am not sure if this is the right part of the forum to ask this question. So I started reading papers about the Lyapunov Exponent, but there is something I do not understand in the formula. Why ? It seems logical that we want because we want to get the Exponent...
  6. A

    Is it Possible to solve Exponential Equations like these?

    Homework Statement Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not? Homework Equations 8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x) The Attempt at a Solution Brought all e^(ax) values to one...
  7. D

    How do I write taylor expansion as exponential function?

    How do I write taylor expansion of a function of x,y,z (not at origin) as an exponential function? Please see the attached image. I need help with the cross terms. I don't know how to include them in the exponential function?
  8. S

    A question regarding the definition of e

    Homework Statement In writing the definition of ##e## i.e. ##e=\displaystyle\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n##, why do we denote the variable by 'n' despite the fact that the formula holds for n∈(-∞,∞)? Is there any specific reason behind this notation i.e. does the variable have...
  9. Y

    Exponential decay

    Homework Statement superman has been disabled by a nearby amount of kryptonite, which decays exponentially. If Superman cannot regain his power until 90% og the kryptonite disintegrates, then how long will it be before he regain his powers? Use r=-0.138629. Round to the nearest day. a. 4days...
  10. M

    Differentiation of an exponential expression

    Homework Statement [/B] I need to differentiate the exponential function i = 12.5 (1-e^-t/CR) and I need to plot a table so that I can do a graph of i against t but i'm not sure how. (CR is the equivelant of Capacitance 20 Micro Fards and Resistance 300 Kilo Ohms) Homework Equations [/B] How...
  11. N

    The graph of an exponential function given by f (x) = A(b^x)+c

    Homework Statement The graph goes through the points (-2, 13) and (0, 5) and has the horizontal asymptote y = 4. f(−2) = ____ therefore: ____(B^____ ) = ____ b = The Attempt at a Solution f(−2) = 13 therefore: 1 (B^-2 ) = 13 b = ? not sure Thank you