Exponential Definition and 1000 Threads

Hello Physics Forums, I sometimes come across statements like this (from http://beige.ucs.indiana.edu/B673/node62.html" ): [FONT="Courier New"]Now assume a solution of the following form: x(t) = Aeat What is the motivation/background to make such an assumption? In this case the equation...

Solve for real-valued x, e-aX + e-bX = 1, where a and b are arbitrary known constants > 0. For example, e-48.12/50 + e-48.12/100 ~ 1.00 In this case X = 48.12 (to two decimals), a = 1/50 and b = 1/100. For any specific values of a and b, a computational solution can easily be determined...

Homework Statement Viruses are reproducing exponentially, while the body eliminates the viruses. The elimination rate is constant, 50000 per hour. I decided to take down on the minute level, so it would be 50000/60. Pinitial is 10^6 k is ln(1,6)/240, since the growth rate is 160% in 4...

Homework Statement Viruses are reproducing with rate of k ,in t minutes, the function is: f(x) = Po x e^(kt) However there is an elimination rate of a viruses per minute. Homework Equations The Attempt at a Solution We can't say that the new function will be: f(x) = Po x e^(kt)...

It is known that \[\sum\limits_{k = 0}^\infty {\frac{{N^k }} {{k!}}} = e^N \] My question is \[\sum\limits_{k = 0}^M {\frac{{N^k }} {{k!}}} = ? \] where $M\leq N$ an integer. This is not an homework

Homework Statement e^(2x+9) - 4e^x -5 = 0 Homework Equations The Attempt at a Solution I changed this into: e^(2x+9) =4e^x + 5 I took logarithm of both sides: 2x+9=ln(4e^x +5) but i don't know what to do with the right hand side. what will be the easiest way to solve this...

Homework Statement A=\begin{bmatrix}-1 & 2 & 0\\-2 & -1 & 0\\ 0 & 0 & -3\end{bmatrix} Use matrix A and compute exp(tA) explicitly. Homework Equations I am having trouble figuring out how to start this. I know how to look at each component of matrix A and to use exp(tA)=I+tA...

Homework Statement Integrate the following equation for average energy from -infinity to infinity \int(c*x^4)*(e^(-c*x^4)/KT)dx Homework Equations c, K, T are constants \int(e^(-c*x^4/KT)) = (KT/c)^(1/4)*(2\Gamma(5/4)) The Attempt at a Solution I tried using integration by parts...

Homework Statement let be A_{i,j} a Hermitian Matrix with only real values then \int_{V} dV e^{iA_{j,k}x^{j}x^{k}}= \delta (DetA) (2\pi)^{n} (1) Homework Equations \int_{V} dV e^{iA_{j,k}x^{j}x^{k}} = \delta (DetA) (2\pi)^{n} The Attempt at a Solution the idea is that...

Need help solving this. \int^{\infty}_{-\infty} e^{\frac{-x^{2}}{\sigma^{2}}} e^{-ikx}dx That's the integral of the product of the exponentials , couldn't get latex to make it look right. Supposedly usefull information(I can't see how); \int^{\infty}_{-\infty}...

Its true that if you integrate an exponential function from some time t0 to infinity it will converge to a finite value. However, is the same true if it is multiplied by say t, t^2, t^3,t^n. i.e. t*exp(-t) for example. the exp is decaying to zero faaster than t is, so it goes to zero...

Homework Statement Suppose two exponential functions, f(x) and g(x) are symmetric with respect to x = 2. f(x)=a^{bx-1} g(x)=a^{1-bx} Prove f(2) = g(2) Homework Equations The Attempt at a Solution This isn't actually a problem. This is a property used to solve a different...

Is the series \sum_{n=0}^{\infty}\frac{z^n}{n!} uniformly convergent for all z in the complex plane? It is uniformly convergent for all z in any bounded set, but the complex plane is unbounded. My instinct is that it is NOT uniformly convergent for all z in C. This is not homework.

Hi folks, hope somebody can help me understand this one please? Gven an expression i = ia-ic = icorr(exp(n/Ba)-exp(-n/Bc)), we are told that if -n<<Bc then exp(-n/Bc) tends to 0 & the equation becomes i (is approx) = ia = icorr exp(n/Ba). I find that exp(-n/Bc) tends towards 0 if I...

let be the exponential sum S= \sum_{n=1}^{N}e( \frac{f(x)}{p}) e(x)= exp( 2i \pi x) my conjecture is that since the complex exponential takes its maximum value '1' when x is equal to an integer then Re(S)= \Pi (f,N) with \Pi (f,N) is the number of solutions on the interval...

Homework Statement I am in the process of doing a physics problem with a differential equation that has the form: y = Acos(kx) + Bsin(kx) According to my notes, this can also be written as y =Aejkx + Be-jkx, unfortunately I just don't see how to write the original equation like that...

Homework Statement Series k=1 to k=Infinity of: k^2/k! a) e b) 2e c) (1+e)(e-1) d) e^2 e) Infinity Homework Equations e^x = Series from n=1 to n=Infinity of: x^n / n! The Attempt at a Solution I was guessing this would end up being C but the answer is infact B. As...

Exponential Attenuation and Beta Particle Range (solved) Homework Statement I am given a beta emitter and its atomic mass, as well as the atomic mass of its daughter, which have a difference of 0.0034 amu. I am to determine the range of the particles in air. Homework Equations I am given...

Homework Statement 1) 5x+4-5x-1<24 2) 2x+2-1>=22x+3 3) 21-x-2x+1/2x-1<0 Homework Equations At the 2nd I do like this: 2x+2-22x>=4 divide by 2 2x+1-22x-1>=2 x+1-2x+1>=1 -x>=-1 divide by (-1) x=<1 but when i put 0 in x the inequation is incorrect, what I have mistake, please...

Homework Statement Please , can anybody help me to do these and to explan to me? I tried tried, but i can't do anything. 1. 4x-1 + 4x + 4x-1=84 2. 15 * 2x+1 + 15 * 2 x-1 =135 3. 8x + 18= 2* 27x 4. 3x-8*3x/2 +15=0 5. 5x - 53-x=20 Homework Equations At the 5th i do...

Homework Statement Howdy, Given a matrix \left[\begin{array}{ccc}x_{11} & x_{12}\\x_{21} & x_{12}\end{array}\right] Which has the exponential matrix e^{t\cdot a} When given the eqn x'= Ax + b where b = \left[\begin{array}{c}b_1 \\ b_2\end{array}\right] I know that had it only...

Suppose I have a sample X_1, ..., X_n of independently, identically distributed exponential random variables. One result I deducted was that the ratio of any two of them (eg. X_1 / X_2) is independent of the sample average 1/n * \sum_{i=1}^{n} X_i. (Aside: that ratio, as a random variable...

Hi, can I do the following? If I am asked to find as lim x -> inf of (3^n/2^n), can I do: 3^n = e^(n*ln3) 2^n = e^(n*ln2) assume C = lim (3^n/2^n). C = lim e^(n*ln3)/e^(n*ln2) ln C = lim ln [(exp(n*ln3)/(exp(n*ln2)] In C = lim ln(exp(n*ln3)) - ln(exp(n*ln2)) ln C = lim n*ln3 -...

Can someone please tell me if I have the correct answer for this one? e^(5pi/4) = (1-i)/(-sqrt(2)) Thanks...

Can anyone show me how to solve the following equations: 2^(x-1)-2^(x)=2^(-3) 3^(x+1)+3^(x)=36 I would greatly appreciate your assistance.

Homework Statement For each n \in \mathbb{N}, let f_n(x) = e^{nx} for x \in \mathbb{R}. Prove that f_1, ... , f_n are linearly independent vectors in {\cal F}(\mathbb{R}, \mathbb{R}) Homework Equations The Attempt at a Solution I know that the simple way to prove this for n=2...

Hey, I'm having trouble starting this assignment. If you could just tell me how to get started and the path I should be on then that would be great and I can do the rest. Here are the questions: 1) Solutions to x= - x^k for x0>0 satisfy x(t) goes to 0 as t goes to infinity. Characterize the...

Hi guys, I lurk here often for general advice, but now I need help with a specific concept. Ok, so I started a classical and quantum waves class this semester. We are beginning with classical waves and using Vibrations and Waves by A P French as the text. So in the second chapter he discusses...

Homework Statement Solve. Q 1.) 3^{3x}+3^{3x+2}=30 Q 2.) 3^{2x}-12(3^{x})+27=0 Homework Equations (a^{n}){b}=a^{nb} a^{n}(a^{b})=a^{n+b} The Attempt at a Solution Q 1.) 3^{3x}+3^{3x+2}=3^{1}+3^{3} Q 2.) 3^{2x}+3^{3}=12(3^{x}) 3^{2x}+3^{3}=(3^{1}+3^{2})(3^{x})...

first i had to show solve x′=sin(x) to get t=ln|(csc(x₀)+cot(x₀))/(csc(x)+cot(x))| i did that. next i need to show that for x₀=(π/4) you can solve x=2arctan(((e^{t})/(1+√2))) what I've done so far is t=ln|((csc(pi/4)+cot(pi/4))/(csc(x)+cot(x))| t=ln|((2/sqrt(2)+1)/(csc(x)+cot(x))|...

Homework Statement d/dT (e-E0/(kT)) Homework Equations d/dx(ex) = ex The Attempt at a Solution e-E0/(kT) * E0/kT2 ? Do you use the chain rule on the exponent of e?

The inverse of the exponential function... Homework Statement Find the inverse of the function = e ^ (x^3) Homework Equations The inverse of the exponential function = the natural logarithm of that same function The Attempt at a Solution inverse of f(x) = ln(x^3) ? This...

Hey I'm new here. I got a quick question about the e^x function. I was noodling with my graphing calculator and noticed that every time i took the integral of (x+1) I kept getting a graph that was closer to the graph of e^x. So after this I took the integral of (x+1) about 10 times and got an...

r(cos u + i sin u) t(cos v + i sin v) How do I convert these into exponential form using Euler's Theorem?

if f(x) = pi*xe^(-x^2) integrating this function if the lower boundary is 0 and the upper boundary is infinity is the answer pi*(2e-1). is this right?

Homework Statement expand the exponential term in the equation y=2[e^{x+(x²/2)}-1] as a power series Homework Equations on wikipedia I found this... http://img297.imageshack.us/img297/1088/15139862vw6.jpg The Attempt at a Solution Do I substitute x+(x²/2) as "x" in the above...

log8(9y+14)=6x6-11 9y+14=86x6-11 ln(9y+14)=ln86x6-11 ln9y+ln14=(6x6-11)ln8 ln9y=(6x6-11)ln8-ln14 y=((6x6-11)ln8-ln14)/ln9 is this equation correct??

Homework Statement Solve the following: Question 1: \sqrt[5]{256}\div\sqrt[6]{64}=2^{x} Question 2: \frac{(9^{2x-1})^{3}(3^{3x})^{2}}{(27^{x+2})^{4}}=81^{3} Homework Equations None that I am aware of. The Attempt at a Solution Question 1: \sqrt[5]{2^{8}}\div2^{1}=2^{x} Question 2...

Cool lecture on exponential growth http://sciencehack.com/videos/view/F-QA2rkpBSY The video shows how to calculate the doubling time by dividing 70 by the growth rate. So for a 7% growth rate, the doubling time is 10 years.

Q: If X_1 and X_2 are independent exponential random variables with respective parameters \lambda_1 and \lambda_2, find the distribution of Z = X_1 / X_2. Discussion The best method to attack this problem apparent to me is coming up with a cumulative distributive function for Z and then...

The question is: if X is an exponential random variable with parameter \lambda = 1, compute the probability density function of the random variable Y defined by Y = \log X. I did F_Y(y) = P \{ Y \leq y \} = P \{\log X \leq y \} = P \{ X \leq e^y \} = \int_{0}^{e^y} \lambda e^{- \lambda x} dx =...

Homework Statement In the standard model for exponential decay, y=ab^x , what does a represent and why? The Attempt at a Solution I know that a is the value of y when x=0, but I don't understand why this is the case. Any help would be appreciated, thanks.

Homework Statement Prove that sinh(kt) is of exponential order |k|. Find M>0, c>=0 and T>0 to show that |f(t)|= Me^(ct), t>T Homework Equations |f(t)|= Me^(ct), t>T The Attempt at a Solution I'm looking at the graph of sinhkt (i graphed a few values of k) and indeed it is of an...

Homework Statement I've never understood e^{i\theta} very well. I know that e^{i\theta} = cos \theta + i sin \theta, but how about e^{4i}? Would this be cos 1 + 4i sin 1 or cos 4 + i sin 4? What's the general rule for these kinds of numbers? Homework Equations e^{i\theta} = cos \theta...

hello! there's this question I am working on and I am mostly through it (well, I hope I am at least), there's just one or two things still annoying me/need confirmation. Here's the question: 50 coins were flipped. For every coin that landed with the head showing upwards, it was taken away...

Does anyone know how to differentiate an exponential, which has an operator in its power? I found it quite a trouble in Peskin's QFT (page 84, formulas (4.17), (4.18)). Here we have these two formulas of Peskin: U\left( t,t_{0}\right)=e^{iH_{0}\left( t-t_{0}\right) }e^{-iH\left(...

Pdf (or mgf) of maximum of dependent exponential random variables ? max of Z1, Z2, Z3, Z4 where Z1 = |X1+X2+X3|^2 + |Y1+Y2+Y3|^2 Z2 = |X1-X2+X3|^2 + |Y1-Y2+Y3|^2 Z3 = |X1+X2-X3|^2 + |Y1+Y2-Y3|^2 Z4 = |X1-X2-X3|^2 + |Y1-Y2-Y3|^2 Xi, Yi are independent zero mean normal with...

Hi, I have had this question for some time now and I am really struggling to find any information on the topic. So here it is, By research find out how an exponential function can be found by first obtaining a function using logarithms and then graphing. Show and explain why this...

Hello all, I can't believe I having a hard time with this problem but...I am :cry:1. 2^(x^2) X 4^(2x) = 1/8 2. make the bases the same? 3. 2^(x^2) X 2^((2x)^2) = 1/8 2^(3x^(2)) = 1/8 3x^(2)log2=log1/8 (log1/8)/(log2) = 3x^(2) x^(2) = -1 I know I am doing it wrong. Any help would be greatly...

Homework Statement f(x)=(((x^7)+3)((x^3)+2)) / (((x+3)^2)((x^6)+5)) Find f'(x) Homework Equations d/dx lnx = 1/x d/dx ln(f(x)) = f'(x)/f(x) The Attempt at a Solution ln(f(x)) = ln((x^7)+3) + ln((x^3)+2) - ln((x+3)^2) - ln ((x^6)+5) f'(x)/f(x) = (7x^6)/((x^7)+3) +...