Exponential Definition and 1000 Threads

  1. jdawg

    Exponential Graph: Is Square Root an Exponential?

    Homework Statement Is a function that has a square root an exponential graph since you can rewrite a square root as x^1/2? Homework Equations The Attempt at a Solution
  2. J

    MHB Exponential and Logarithmic Problem

    I am looking for help solving for x for the question below. Any help would be greatly appreciated. 2^x=16(8^2x)
  3. A

    MHB How to Solve Exponential Equations?

    Hi, I attached a pdf with a question and its answers. I don't understand the whole thing basically, e.g what their asking for.. 1.2.1;1.2.2;1.2.3 1.2.2 - How many solutions for x will the equation have..? 1.2.3 - Largest integer for which it will have solutions..? Any explanations will...
  4. KevinMWHM

    How Do You Calculate the Decay Rate of C14 with a Given Half-Life?

    Doing some self prep for Diff EQ starting next week. Determine the decay rate of C14 which has a 1/2 life of 5230. Using e^kt as a function, I solve using k5230=ln.5 which gives the obvious answer of negative what I want. How do I know to use the reciprocal (ln2) other than to "just know" I...
  5. V

    Effects of Load on Diode Circuit with Exponential Model

    Homework Statement The circuit in the diagram utilizes three identical diodes having I_S = 10−16 A. Find the value of the current I required to obtain an output voltage V_o = 2.4 V. If a current of 1 mA is drawn away from the output terminal by a load, what is the change in output...
  6. T

    Derivation of the exponential distribution - that infinitesimal

    Hello, I've been looking at the derivation of the exponential function, here http://www.statlect.com/ucdexp1.htm amongst other places, but I don't get how, why or what the o(delta t) really does. How does it help? It's really confusing me, and all the literature I've looked at just...
  7. B

    Integrating power of a cosine times a complex exponential

    Homework Statement Consider the inner product $$\frac{1}{2\pi}\int_0^{2\pi} \left(\frac{3}{5 - 4\cos(x)}\right) e^{-ikx} dx, \quad k \in \mathbb{Z}, \quad x \in \mathbb{R}.$$ Homework Equations Is there a method to solve this without using the residue theorem, e.g. integration by parts...
  8. M

    How Do Exponential and Radical Properties Solve Textbook Problems?

    So this is what I have tried so far playing around with exponent and radical properties to try and solve this textbook problem
  9. polygamma

    MHB Evaluating an Integral with Exponential Factors

    Show that for $a >0$ and $b \ge 0$, $$\int_{0}^{\infty} e^{-a^{4}x^{2}(x^{2}-6b^{2})} \cos \Big(4a^{4}bx(x^{2}-b^{2}) \Big) \ dx = \frac{e^{a^{4}b^{4}}}{4a} \Gamma \left( \frac{1}{4} \right) $$
  10. U

    Eigenvalues and Eigenvectors of exponential matrix

    Homework Statement Part (a): Find the eigenvalues and eigenvectors of matrix A: \left( \begin{array}{cc} 2 & 0 & -1\\ 0 & 2 & -1\\ -1 & -1 & 3 \\ \end{array} \right) Part(b): Find the eigenvalues and eigenvectors of matrix ##B = e^{3A} + 5I##. Homework Equations The Attempt at a Solution...
  11. L

    Proving an exponential function obeys the wave equation

    Homework Statement Prove that y(x,t)=De^{-(Bx-Ct)^{2}} obeys the wave equation Homework Equations The wave equation: \frac{d^{2}y(x,t)}{dx^{2}}=\frac{1}{v^{2}}\frac{d^{2}y(x,t)}{dt^{2}} The Attempt at a Solution 1: y(x,t)=De^{-u^{2}}; \frac{du}{dx}=B; \frac{du}{dt}=-C 2...
  12. S

    Exponential potential for inflation

    hi I want to solve inflation problem for exponential potential. v(\phi) = v_0 exp(-\alpha \phi) (it's known as barrow or pawer law inflation ) we have 2 main equations: H^2 = 8π G / 3 (1/2 (\dot{\phi})^2 + v(\phi)) \ddot{\phi} + 3H \dot{\phi} + v(\phi)'=0 I must solve this 2 equ...
  13. T

    What is the Correct Notation for Logarithmic Equations?

    Homework Statement (2^(x+1)) / (5^x)) = 3 2.The attempt at a solution (2^(x+1)) / (5^x)) = 3 ((log 2 (x+1)) / (x log 5)) = log 3 (x log 2 + log 2) / (x log 5) = log 3 ( log (2^ (x+1))) / (log (5^x)) = log 3 log (base: 5^x) (number: 2 ^ (x+1)) = log 3 (5^x) ^ (log 3) =...
  14. G

    Commutator of exponential operators

    How do I compute the commutator [a,e^{-iHt}], knowing that [H,a]=-Ea? I tried by Taylor expanding the exponential, but I get -iEta to first order, which seems wrong.
  15. 1

    Exponential formulation of waves

    Hi all, I'd just like to clear up something that's often confused me. In classes (particularly classical waves/QM) we've often seen the lecturer switch from describing a wave as (most commonly) Acos(kx-{\omega}t) to e^{i(kx-{\omega}t)} but doesn't the exponential representation include an...
  16. G

    Can the inverse of a matrix exponential be proven using its definition?

    I have to prove the inverse of the matrix e^A. we haven't studied exponential matrices in uni but he gave us the definition of it with the series e^A= I+A+A^2 ... A^k where A^k=0, even for numbers greater than k. I have tried to think of a way to prove it, but neither my classmates or I found...
  17. C

    How Do You Find the Inverse of an Exponential Matrix?

    We have a matrix with dimension NxN.For some m belongs to N,m0 we have A^m0=0.We consider the exponential matrix e^A=I+A+A^2/(2!)+A^2/(3!)+A^m/(m!).Find the inverse matrix of e^A. I tried to write the e^A=e^A(m0)+A^m/(m!) or (e^A)^(-1)=(...
  18. R

    Exponential least-squares fitting and initial parameters

    Dear All, I would like to do an exponential function least-squares fitting, but having two or more exponents. For example the function looks like this: y (x) = A \exp (-x/a) + B \exp (-x/b) where A, a, B and b are the least-squares fitted parameters. My question is how to obtain the...
  19. M

    Integrating an exponential function over [itex]|x|+|y| \leq 1[/itex]

    OK, I'm new to multi-variable calculus and I got this question in my exercises that asks me to integrate e^{-2(x+y)} over a diamond that is centered around the origin: \int\int_D e^{-2x-2y} dA where D=\{ (x,y): |x|+|y| \leq 1 \} I know that the region I'm integrating over is symmetric...
  20. J

    Identifying Exponential Growth or Decay in (e^4-x) + 2

    Homework Statement State whether (e^4-x) + 2 is an exponential growth function or an exponential decay function. Explain why. Homework Equations I want to use the formula f(x) = ae^kx where a>0, and k<0. The Attempt at a Solution I know it is an exponential decay formula...
  21. J

    Logarithmic and exponential equations

    Homework Statement (2^x - 2^-x)/3=4 Homework Equations Using log or exponential rules The Attempt at a Solution First multiply both sides by 3 so 2^x-2^-x=12 I thought I could take the log of both sides then condense the log, but that is not right. I also attempted to...
  22. A

    Exponential Distribution with Probability

    $$f(y) = \begin{cases} 0& \text{for }y< 0,\\ 2y& \text{for }0 ≤ y ≤ .5,\\ 6-6y& \text{for }0.5 < y ≤ 1, \\0& \text{for } y > 1\end{cases}$$ (1) Find cumulative distribution function, F(y) $$F(y) = \begin{cases} 0& \text{for }y< 0, \\\int_0^y 2t dt = y^2 & \text{for } 0 ≤ y ≤ .5,\\.5^2+...
  23. A

    Exponential Distribution with Probability

    $$f(y) = \begin{cases} \int_0^y\frac1\beta e^{\frac {-t}\beta}dt = -e^{\frac {-y}\beta}+1 & \text{for } 0 ≤ y < ∞,\\ 0& \text{for } elsewhere\end{cases}$$ P(Y>3) = 1 - P(Y ≤ 3) = 1 - (-e^{-3/beta}+1) = .1353 When I take log to both sides, I get 3.453. When I take ln to both sides, I get...
  24. A

    Exponential distribution moment generating function to find the mean

    With mean = 2 with exponential distribution Calculate E(200 + 5Y^2 + 4Y^3) = 432 E(200) = 200 E(5Y^2) = 5E(Y^2) = 5(8) = 40 E(4Y^3) = 4E(Y^3) = 4(48) = 192 E(Y^2) = V(Y) + [E(Y)]^2 = 2^2+2^2= 8 E(Y^3) = m_Y^3(0) = 48(1-2(0))^{-4} = 48 is this right?
  25. A

    Application for exponential distribution

    The amount of time to finish a operation has an exponential distribution with mean 2 hours Find the probability that the time to finish the operation is greater than 2 hours. My thinking is to integrate the exponential probability function. After integrating it, I got -e^{-y/2} + 1 , 0 ≤ y...
  26. M

    Example of Probability Distribution Not in Exponential Family

    Is there a good example of a probability distribution where the support set does not depend on the parameters and is still not a member of the exponential family?
  27. C

    MHB Solve Exponential Equation: 2+√2^x + 2-√2^x =4

    Hi, I'm having problems to solve this equation, pls help me: \left( 2+\sqrt {2}\right) ^{x}+\left( 2-\sqrt {2}\right) ^{x}=4
  28. J

    Wish to solve exponential congruence equation

    Hi, Is it possible to find a value of ##n## for the following expression other than by exhaustive search? $$e^{\frac{2n\pi i p}{q}}=e^{-\pi i p/q},\quad n=1,2,\cdots, q-1, \quad (p,q)\in \mathbb{N}\backslash 0$$ I can write a short program to search for the value of n, but that would...
  29. P

    MHB Exponential Func: Solving ln6=ln2+ln3

    Hello everyone, I was solving this problem: Justify that ln6= ln2+ln3 So: exp(ln2+ln3)=exp(ln2)*exp(ln3)= 2*3= 6 = exp(ln6) Till here, my work was okay. What I didn't understand is : why should we say that the exponential function is strictly increasing over R before being able to simplify the...
  30. P

    Integration with exponential and inverse power

    I confront an integration with the following form: \int d^2{\vec q} \exp(-a \vec{q}^{2}) \frac{\vec{k}^{2}-\vec{k}\cdot \vec{q}}{((\vec q-\vec k)^{2})(\vec{q}^{2}+b)} where a and b are some constants, \vec{q} = (q_1, q_2) and \vec{k} = (k_1, k_2) are two-components vectors. In the...
  31. N

    MHB Geometric rv and exponential rv question

    Please refer to the attached image.for part a) this is what i did: $G = k$, $k-1< X < k$ so I substituted $k-1$ and $k$ into the given exponential rv, this gave me $\lambda e^{-\lambda(k-1)}$ and $\lambda e^{-\lambda k}$ $= \lambda e^{-\lambda(k-1)} + \lambda e^{-\lambda k}$ But I...
  32. J

    Solve Exponential Equation: 2^x·ln(2)+3^x·ln(3)+4^x·ln(4) = 2x

    No. of Real solution of the equation ##2^x\cdot \ln (2)+3^x\cdot \ln (3)+4^x\cdot \ln (4) = 2x## . The attempt at a solution Let ##f(x) = 2^x\cdot \ln (2)+3^x\cdot \ln (3)+4^x\cdot \ln (4) -2x## Here solution must be exists for ##x>0##, because for ##x\leq 0##, L.H.S>0 while R.H.S <0...
  33. I

    MHB Exponential Growth & Decay Question

    Suppose that there is initially x(not) grams of Kool-Aid powder in a glass of water. After 1 minute there are 3 grams remaining and after 3 minutes there is only 1 gram remaining. Find x(not) and the amount of Kool-Aid powder remaining after 5 minutes… So, i set up 2 equations… 3=x(not)e^-k(1)...
  34. C

    MHB Implicit differentiation with exponential function

    find dy/dx: exy+x2+y2= 5 at point (2,0) I'm confused with finding the derivative with respect to x of exy. this is what I did so far for just this part: exy*d(xy)/dx exy*(y+x*dy/dx) do I need to put the parentheses on here? I thought so because that is the part where I used the product rule...
  35. J

    MHB No. of real solutions in exponential equation

    no. of real solution of the equation $3^x+4^x+5^x = x^2$
  36. J

    Equation with two unknowns in complex exponential

    hello friends, when i build the mathmatical model of robot,i face a new question that i ever seen before. i have a reverse kinematic lever as the leg and i want to use the tip position to get the relationship of fold angle and rotate angle reversely here is my equation: x*e^iθ - y*e^iθ *...
  37. M

    How Do You Calculate P{S < t < S + R} for Independent Exponential Variables?

    Hi, I have a quick question. Let R and S be two independent exponentially distributed random variables with rates λ and μ. How would I compute P{S < t < S + R}? I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R...
  38. C

    Exponential functions word problem

    Homework Statement The function T=190(1/2)^1/10t can be used to determine the length of time t, in hrs that milk will remain fresh. T is the storage temp. In Celsius How long will milk remain fresh at 22 degrees Celsius Homework Equations Bases have to be same then exponents will...
  39. T

    What does living in exponential times mean?

    What does living in exponential times mean?
  40. G

    Exponential Distribution and Waiting Time

    Homework Statement Suppose that the waiting time for the CTA Campus bus at the Reynolds Club stop is a continuous random variable Z (in hours) with an exponential distribution, with density f(z) = 6e–6z for z ≥ 0; f(z) = 0 for z < 0. (a) What is the expected waiting time in minutes (the...
  41. M

    Solving logarithmic and exponential equations

    Homework Statement I'm trying to solve trying logarithmic and exponential equations but for the life of me I can't seem to figure out what I'm doing wrong. Homework Equations Log equation: log3(x+2)+1 = log3x²+4x Exp equation: 2x + 2x+1 = 3 The Attempt at a Solution For the first...
  42. Y

    Is j^{-p}=e^{-j\frac{p\pi}{2}} a valid exponential function?

    Homework Statement I want to verify j^{-p}=e^{-j\frac{p\pi}{2}} Homework Equations e^{j\frac{\pi}{2}}=\cos(\frac{\pi}{2})+j\sin(\frac{\pi}{2})=j The Attempt at a Solution j^{-p}=(e^{j\frac{\pi}{2}})^{-p}=e^{-j\frac{p\pi}{2}} Am I correct? Thanks
  43. S

    MHB Transforming an integral of Exponential to a Contour

    Hi friends, i need some help for this number: By considering the integral $$\int_{\gamma(0;1)}\exp(z) \mathrm{d}z$$,show that $$\int_0^{2\pi}\exp(\theta)\cos(\theta+\sin(\theta)) \mathrm{d}\theta = 0$$ i know that since $$f(z)=\exp(z)$$ is holomorphic on and inside...
  44. M

    Solving Exponential Integral Homework

    Homework Statement The problem says: u = 8[exp(y) - 1] Homework Equations The Attempt at a Solution Does this mean: 8ey-1 or 8ey-1
  45. C

    MHB Find derivative with exponential function?

    f(x)=x2ex the answer is f'(x)=(x2 + 2x)ex but I don't understand how to get there. Also I need to find g'(x) if g(x)=sqrtx(ex) would the answer for the second one be .5x-1/2ex?
  46. X

    How Can You Solve 10^x = 2 Without a Calculator?

    So, if we start with logarithm ln(2) assuming a base of 10, how would I solve this without a calculator? ln(2) 10^x = 2 And I get stuck there without a calculator. I could .. ln(10^x) = ln(2) x ln(10) = ln(2) x = ln(2) But that gets me back to where I started. So, how would I go...
  47. paulmdrdo1

    MHB Integration of exponential function

    just want to confirm if i did set up my integral correctly and got a correct answer. $\displaystyle\int_0^a (e^{\frac{x}{a}}-e^{-\frac{x}{a}})$ using substitution for the first term in my integrand $\displaystyle u=\frac{x}{a}$ $\displaystyle du=\frac{1}{a}dx$; $\displaystyle dx=adu $ for...
  48. J

    Real Solutions of Exponential Equations ##e^x = x^2## & ##x^3##

    [1] Total no. of real solution of the equation ##e^x = x^2## [2] Total no. of real solution of the equation ##e^x = x^3## My Solution:: [1] Let ##f(x) = e^x## and ##g(x) = x^2## Now we have use Camparasion Test for derivative So ##f^{'}(x) = e^x## which is ##>0\forall x\in...
  49. R

    Finding Electric Field of Exponential Charge Distribution

    Homework Statement I am to find the electric field for a charge distribution of $$ \rho(x)= e^{-\kappa \sqrt{x^2}} $$ Homework Equations I know that gauss law is $$ \int E \cdot da = \frac{q_{enc}}{\epsilon_0} $$ The Attempt at a Solution I am not sure what the charge...
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