Exponential Definition and 1000 Threads

I'm rather confused on how to operate exponents on fractions. For example (4/3)^-1 or (4/3)^1 Please explain?

I got a question here, and I am stuck at understanding the step of the solution. Any help will be appreciated. http://img841.imageshack.us/img841/6589/40155869.jpg I would like to know how to get from the second to the third step, where the summation comes in. It looks like multiplication of...

I am trying to understand the physics of an exponential horn. I got most of my references online and according to the Horn Physics by Martin King, the volume velocity at the mouth is greater than the applied volume velocity at the throat (the horn is driven by a speaker/buzzer). This is what i...

Hi everyone, There's something that's kind of been bugging me about applying exponential decay formulas to real world phenomena. For example let's say the discharging of a parallel plate capacitor. Let's consider the negative plate. As it discharges excess electrons leave the plate. The...

Homework Statement im wondering if e^i(x+y) + e^-i(x+y) can be simplified to 2cosxcosy Homework Equations 2cosx= e^ix + e^-ix so i separated e^i(x+y) + e^-i(x+y) into; e^ix(e^iy) + e^-ix(e^-iy) can that become 2cosxcosy?

Homework Statement Determine the limit and then prove your claim. limx\rightarrow\infty (1+\frac{1}{x^2} }) xHomework Equations I know that the formal definition that I need to use to prove the limit is: {limx\rightarrow\infty (1+\frac{1}{x^2})x=1}={\forall \epsilon>0, \exists N > 0, \ni x>N...

We know how to solve problems like e^ax+e^bx=k, when a=2b. But how to solve equations of this type when a is not equal to 2b?

Hi, I'm in a signal processing class, and I'm having some trouble with complex numbers. As an example, I've attached a pretty simple question about an exponential Fourier series. I don't find these questions particularly hard, it just takes me ridiculously long to do them. I mean, after I...

Homework Statement Find the exact value of P(|Y- μ| < 1.4σ) for an exponential random variable with parameter β. Homework Equations The only equation that I can think of is the exponential distribution equation: ∫(1/β)e^(-y/β) The Attempt at a Solution I have been unable to...

Hi, I have a conceptual question. Looking at exponential smoothing methods I came across relationship between the autocorrelation function and lambda. It says that if the time series doesn't apper to be autocorrelated then lambda is expected to have a low value :confused: .Any help will be...

Homework Statement Consider a Poisson process for which events occur at a rate of 2 per hour. (a) Give the probability that the time until the first event occurs exceeds 2 hours. Use an exponential distribution to find the probability.Homework Equations The Attempt at a Solution \lambda = 1/2...

1.\frac{dx}{dt}= \stackrel{9 -12}{2 -1} x(0)=\stackrel{-13}{-5} So I seem to be having issues with this problem There are 2 eigenvalues that I obtained from setting Det[A-rI]=0 That gave me r^{2}-8r+15=0 solving for r and finding the roots i got (r-3)*(r-5)=0 so the...

Homework Statement I need to use the relation exp(i*Pi/4) = (1+i)/sqrt2 but I'd like to know where it came from. I am clueless about how to arrive at this.

- exp(f) = Laplacian(f) where f is a real valued function of two variables in an open domain.

The problem is (\sqrt[4]{6x})^3 And i have to convert it to exponential form, and I forgot how to do this, so i need some help. Thank you.

Hello, Suppose you observe some foam. The foam is formed by a set of bubbles, and each bubble blows up after a random time. The density function of the time each bubble will take to blow up is probably exponential, with rate lambda. The total amount of foam (Q) must also decay exponentially...

Homework Statement At how many points in the xy-plane do the graphs of y=x^{12} and y=2^{x} intersect? Homework Equations none The Attempt at a Solution I have no idea what to do. I thought of trying to narrow it down to some intervals where the graphs may cross, but, since they're...

Homework Statement Solve y''(t) - k^2 y(t) = e^{-a|t|} where a and k are both positive and real. Homework Equations The solution was obtained trough a Fourier transform. The Attempt at a Solution I got the solution y(t) = \frac{ke^{-at} - ae^{-kt}}{k(a^2 - k^2)} but when i...

D_n=\frac{1}{\pi}\int_0^\pi\sin{(t)}\cdot e^{-i2nt}dt=\frac{2}{\pi(1-4n^2)} I have no idea on how they get from one side of the equation symbol to the other, can i get some tips and tricks ? I have try ed writing sint as an exp function, but i don't feel it gets me anywhere close.

Homework Statement I am searching for a proof of convergence of matrix exponential series. Where I can find it? Thanks! Homework Equations The Attempt at a Solution

Homework Statement let X1, X2,... Xn form a random sample of size n from the exponential distribution whose pdf if f(x|B) = Be-Bx for x>0 and B>0. Find an unbiased estimator of B. Homework Equations The Attempt at a Solution nothing yet. i don't really know where to get started. a...

Homework Statement find the Fourier transform of complex exponential multiplied to a unit step. given: v(t)=exp(-i*wo*t)*u(t) Homework Equations ∫(v(t)*exp(-i*w*t) dt) from -∞ to +∞ The Attempt at a Solution ∫([v(t)]*exp(-i*w*t) dt) from -∞ to +∞...

how to write 1/x in exponential form ?

this is just something has been bugging me for the last few days. it seems like it has a very basic solution. Muons decay randomly, but have a mean lifetime of about 2 us. If I plot the # of muons that decay vs. time (say the axis spans from 0 to 20 us), why is the plot exponential decay...

Homework Statement If I have a matrix M, say 30 5 20 16 How do I calculate M^{1870} mod 101 using Euler's Theorem. Homework Equations I have so far worked out M ^{2} mod 101 to be 91 28 11 53 and thought I could use this as 2x935=1870 The Attempt at a Solution I...

Homework Statement Annoying problem, I recently got a graphing calculator (t1-89) and according to instructions i can calculate the i (interest) on it but each problem before i attempt on a graphing calculator i attempt to solve myself manually without a graphing calculator as a safeguard to...

Homework Statement The question is located here http://i51.tinypic.com/nex2q1.jpg Homework Equations The value I have been given for a) is 5 The value I have been given for b) is 5PI/6 The Attempt at a Solution Note that e^(a + bi) = e^a e^(bi) = e^a (cos b + i sin b). (e^a is...

Homework Statement Water is pumped into a tank. Volume V, is kept constant by continuos flow. The amount of salt S, depends on the amount of water that ahs been pumped in, call it X. ds/dx = -S/V Find the amount of water needed to eliminate 50% of the salt. Take v AS 10,000 gallons...

exponential equation (simple??) x = Ae ^ kt initally (at t = 0) x = 0.2 and when t = 2 then x = 1.5 a) Find A and k b) Find x when t = 1.5 c) How long will it take x to decay to x = 0.01 Really struggling, any help would be greatly appreciated.

Homework Statement \lim_{x \to \infty} \left(e^x-x \right )^{1/x} Homework Equations The Attempt at a Solution Should I be equating this to f(x), taking the log of both sides, using L'Hopital's rule on the resulting indeterminate quotient? If I do that, then I end up with a perpetual...

I need to prove that ez1 x ez2 = e(z1 + z2) using the power series ez = (SUM FROM n=0 to infinity) zn/n! (For some reason the Sigma operator isn't working) In the proof I have been given, it reads (SUM from 0 to infinity) z1n/n! x (SUM from 0 to infinity)z2m/m! = (SUM n,m)...

Homework Statement Problem: find t in the following equationHomework Equations 64000e^{-1600t}+4000e^{-400t}=50000e^{-1000t} The Attempt at a Solution I know the answer: t=6.17\cdot\;10^{-4}s. But I'm struggling with how to get there. This is my attempt: Factorizing down to...

Homework Statement A radioactive substance has a half-life of 20 years. If 8 mg of the substance remains after 100 years, find how much of the substance was initially present. Homework Equations A=A0ekt The Attempt at a Solution I set the equation up so that 8=A0e100k and...

Homework Statement In the 2 following problems they use the term in the brackets differently, in one case its a percentage and in the other case i have no idea where they get the number from, this is what i would like to find out A cell loses 2% of its charge every day C is total charge t...

Homework Statement I have to evaluate P(t)=|<+,n|\exp{\frac{-iHt}{\hbar}}|+,n>|^2 where H=\hbar \omega_0 S_z + \hbar \omega a^+a+\hbar \lambda(a^+S_-+aS_+) and |+,n>=\left( \begin{array}{c} 1\\0 \end{array} \right) Homework Equations Eigenvalues of H are E_\pm =\hbar \omega (n...

Homework Statement i = 12.5(1-e-t/CR) Current = i Resistance = R Capacitance = C Time = t Firstly i had to calculate the current flowing after 0.5s, given a 30k\Omega resistance and a 20µF capacitance.. easily done. Then i had to work out how long it took to reach 10A, so...

I need to write 2 equations that represent the same exponential function with a y-intercept of 5 and an asymptote at y=3. I got y=2^(x+1) + 3 but I don't know how to find the second equation. Can someone please explain this to me. Thanks.

Does anyone know how to prove this? exp(jAt)+exp(jBt)= 2exp(j(A+B)/2)cos((A-B)/2)

I'm sure this integral is easy, but could someone perhaps show the working of: \int e^{i2t} dt between t and 0. I've tried it with trigonometric identities and keep getting lost! Cheers!

Homework Statement Let z=|z|e^{\alpha*i} Using the fact that z*w=|z||w|e^{i(\alpha+\beta)}, find all solutions to z^4 = -1 The Attempt at a Solution Not quite sure how to proceed, except for the obvious step i=z^2=|z*z|e^{i(2\alpha)}= |z*z|[cos(2\alpha)+isin(2\alpha)] Kinda stuck here :s...

Hi, I am having trouble with this exponential limit problem. Homework Statement \lim \ x \rightarrow 0 \ [ e^{-1/x}] Homework Equations Answer: 0 The Attempt at a Solution \lim x \rightarrow 0 e^(-x)^{-1} \lim x \rightarrow 0 e^{-1}^{x}^{-1} I don't think the second step is right...

Hi, I currently need to solve a problem which leads to an equation of the form a*exp(a*x)+b*exp(b*x)-c=0. The difference between a and b can often become very big, like a=1000 and b=1. Therefore numerical algorithms I tried so far, fail to solve this equation. Has anyone got any clues on a...

Hi, besides integration by parts, does anyone know of a simple integration trick to solve the integral (wrt x) of exp(x)*f'(x)?

Homework Statement Let's say A is a 7x7 matrix which is defined as [a b c 0 0 0 0; b a 0 d 0 0 0; c 0 a b e 0 0; 0 d b f 0 e 0; 0 0 d 0 f b g; 0 0 0 d b f h; 0 0 0 0 0 0 0] where semicolon (;) represent a new row and a space is a new column.Homework Equations If y = expm (A*t), where expm...

Homework Statement exp^\prime(0)B=B for all n by n matrices B. Homework Equations exp(A)= \sum_{k=0}^\infty A^k/k! The Attempt at a Solution Obviously I want to calculate the limit of some series, but I don't know what series to calculate. I wanted to try \lim_{h \to...

Homework Statement I am trying the find the derivative of the function: y= (2x-1)^(tan(3x)) Homework Equations Chain rule, in this case: f'(g(h(x))) * g'(h(x)) * h'(x) exponent rule: where (d/dx) a^x = (a^x) ln a The Attempt at a Solution I feel as if to apply the...

Homework Statement A bacteria culture starts with 3000 bacteria. After 3 h, the estimated counting is 48 000. What is the doubling period? The Attempt at a Solution I figured it would look like the half-life formula, so I wrote it as: B = B0(0.5)t/h Then I subbed numbers in: 48...

Homework Statement A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000. How many bacteria were present initially? Homework...

I am trying to compute the inverse Fourier transform numerically (using a DFT) for some complicated characteristic functions in order to compute their corresponding probability distribution functions. As a test case I thought I would invert the characteristic function for the simple exponential...

X1,X2,...,XN are independently identically exponentially distributed with expected value of 5. How can I compute X[bar]n when n=20 and N=1000? Then compute the proportion of values of X[bar]n that lie between 6.99 and 7.01. repeat the above question with n=100 My thoughts so basically...