Exponential Definition and 1000 Threads

Homework Statement t(s) = 1 15 30 45 60 75 90 105 120 135 N(counts) = 106 80 98 75 74 73 49 38 37 22 Consider a decaying radioactive source whose activity is measured at intervals of 15 seconds. the total counts during each period are given. What is...

Homework Statement How many oscillations occur before Mxy decays to approximately 1/3 of its initial value, for a Larmor frequency of 100 MHz and T2 of 100ms?Homework Equations I was learning about how NMR works and about transverse relaxation. According to what I learned, we can express...

Homework Statement A certain type of transistor has an exponentially distributed time of operation. After testing 400 transistors, it is observed that after one time unit, only 109 transistors are working. Estimate the expected time of operation. Homework Equations The Attempt...

Homework Statement Suppose that the velocity v(t) (in m/s) of a sky diver falling near the Earth's surface is given by the following exponential function, where time is measured in seconds. v(t) = 55 (1-e-0.18(t)) Find the initial velocity of the sky diver and the velocity after 6...

Homework Statement Using the complex exponential, nd the most general function f such that \frac{d^2f}{dt^2} = e-3t cos 2t , t all real numbers. Homework Equations I'm having a lot of trouble with this question, my thinking is to integrate once and then one more time...

I am reviewing some material on Laplace Transforms, specifically in the context of solving PDEs, and have a question. Suppose I have an Inverse Laplace Transform of the form u(s,t)=e^((as^2+bs)t) where a,b<0. How can I invert this with respect to s, giving a function u(x,t)? Would the inverse...

Good day! I have a question regarding the law of the ff: $$ \int_0^t h(s) e^{2\beta(\mu(s) + W_s)} $$ where $\beta >0;$ $h,\mu$ are continuous functions on $\mathbb{R}_+$ with $h\geq 0;$ and $W=\{W_s,s\geq 0\}$ is a standard Brownian motion. Thanks for any help.:D

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement A town's population grows at 6.5% per annum. How many are in town now, if there will be 15 000 in 4.5 years? Please explain which of these solutions is best. Or explain a better solution, please. Homework Equations A(t) = Per(t) <- general approach A = P(1+i)t...

Homework Statement So, i am given 3^x(2x) = 3^x + 2x + 1 And i want to solve for x. Homework Equations I only know that the solution is x=1 but i don't know how to get there. The Attempt at a Solution 3^x(2x) = 3^x + 2x + 1 3^x(2x) - 3^x = 2x + 1 3^x(2x - 1) = 2x + 1 3^x =...

Homework Statement I have the derived function: f'(x) = [1/(1+kx)^2]e^[x/(1+kx)] k is a positive constant Homework Equations I need to find the second derivative, which I thought was just the derivative of the exponent multiplied by the coefficient (as you find the...

I ask members here kindly for their assistance. I'm having some confusion over the process of integrating inequalities, in particular for obtaining the series expansion for the exponential function by integration. The text by Backhouse and Holdsworth (Pure Mathematics 2), shows the expansion of...

Homework Statement Waiting time in a restaurant is exponentially distributed variable, with average of 4 minutes. What is the probability, that a student will in at least 4 out of 6 days get his meal in less than 3 minutes? Homework Equations The Attempt at a Solution If I...

In page 11 of http://math.arizona.edu/~zakharov/BesselFunctions.pdf, I am trying to follow the derivation using binomial theorem to get this step: (e^{j\theta}-e^{-j\theta})^{n+2k}≈\frac{(n+2K)!}{k!(n+k)!}(e^{j\theta})^{n+k}(-e^{-j\theta})^kIf you read the paragraph right above this equation...

Hello I am trying to solve this exponential integral, it's quite complicated. Any hints ? \int \frac{2^{x}\cdot 3^{x}}{9^{x}-4^{x}}dxmany thanks

I am trying to evaluate the following integral. Any help would be appreciated. $$\int e^{x^2}dx$$ i tried the following, $$x^2=t$$ $$2xdx=dt$$ $$\int\frac{e^t}{2\sqrt{t}}dt$$ i tried doing by parts but it didn't work

Hi, Homework Statement If the life expectancy of a light bulb is a random exponential variable and equal (on average) to 100 hrs, is λ then equal to 0.01 or to 100? (λ = 1/expectation)

$f(x)=\dfrac {4^x}{4^{x+2}}$ find :$f(\dfrac{1}{2007})+f(\dfrac{2}{2007})+f(\dfrac{3}{2007})+----+ f(\dfrac{2006}{2007})$

Can someone please explain the below proof in more detail? The part in particular which is confusing me is Thanks in advance!

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Hello! What is the integration of the absolute value of e^ix? That is what is ∫|e^ix|^2 equal to? The whole absolute thing got me lost. Thanks in advance.

I'm working with the integral from 0 to infinity of t^(x-1)e^(-atcos(b))cos(atsin(b)) with respect to t. specifically, I'm asked to solve in terms of the gamma function. my question is more of what general technique i should use. all I've been able to do so far is beat it to death using...

A rabbit population satisfies the logistic equation dy/dt=2*10^-7y(10^6-y) where t is the time measured in months. The population is suddenly reduced to 40%of its steady state size by myxomatosis. a) If the myxo' then has no effect how large is the population 8 months later? b)How long will it...

Hello everyone, how are you? I'm having trouble to evalue the following limit: \lim_{x->\infty} (\frac{x}{1+x^2})^x I "transformed" it into e^{ln{(\frac{x}{1+x^2})^x}} and tried to solve this limit: \lim_{x->\infty} x ln{(\frac{x}{1+x^2})} But I have no idea how to solve it correctly. Can...

Can someone explain how these are equivalent. sqrt((-3)^2) = (-3)^2/2 =sqrt(9) and (-3)^1 3 is not equal to -3 (-3)^2/2 can be expressed as: (-3^2)^1/2 and (-3^1/2)2 (9)^1/2 and (sqrt(-1)sqrt(3))^2...

the half life of C14 is 5730 years. if a sample of C14 has a mass of 20 micrograms at time t = 0, how much is left after 2000 years? I learned from somewhere that these exponential decay and half life problems use the equation y = ab^t or y = a(1+r)^t where y = total, a = initial...

Homework Statement [10] The air pressure in an automobile's spare tire was initially 3000 millibar. Unfortunately, the tire had a slow leak. After 10 days the pressure in the tire had declined to 2800 millibar. If P(t) is the air pressure in the tire at time t,then P(t) satises the di...

I'm looking for the expected value of an exponential Gaussian Y=\text{exp}(jX) \text{ where } X\text{~}N(\mu,\sigma^2) From wolframalpha, http://www.wolframalpha.com/input/?i=expected+value+of+exp%28j*x%29+where+x+is+gaussian E[Y]=\text{exp}(j^2\sigma^2/2+j\mu) If I were to use the...

Homework Statement If f(x) = e^{3x^2+x} , find f'(2)Homework Equations f'(x) = a^{g(x)}ln a g'(x)The Attempt at a Solution f'(x) = (e^{3x^2+x})(ln e)(6x+1) f'(2) = (e^{3(2)^2+2})(ln e)(6(2)+1) = 2115812.288 I was checking online and I'm seeing a different answer, but this is EXACTLY how...

So in my math class we're studying derivatives involving ln(), tanh, coth, etc.. I need to say this first. I skipped precalc and trig and went straight to calculus, so whenever I see a trig problem, I can only go off of what I've learned "along the way." This problem has baffled me, please...

Hi, I need to find out how to plot my data with exponential binning. To better see the exponent of f(x) = x ^ \alpha, where x and f(x) are given, I am asked to do exponential binning the data. Would appreciate you help. Yours Atilla

Any help is appreciated, thanks. Homework Statement In my course of differentials equations we were given the task to model a real life system with them, we choosed something that resembles a pendulum.Homework Equations The Attempt at a Solution We went to the lab and got experimental data from...

If I have ln(e^(-8.336/10c)) wouldn't that be the same as ln(e^(1/(8.336/10c))) therefore = 1/(8.336/10c) = 10c/8.336? I am confused about this because in my lecture notes they simplified ln(e^(-8.336/10c)) to just = -8.336/10c :confused: Your help would be appreciated!

I wasn't quite sure where to put this, so here goes: I am trying to find out some facts about the group SO(2,1). Specifically; Is the exponential map onto? If so, can the Haar measure be written in terms of the Lebesgue integral over a suitable subset of the Lie algebra? What is that subset...

Hi folks could someone please check my calculations contained in attached file? thanks. (incidentally, how can i create a link to such files in the future, weaving them into my text?) Deus(has gone)

Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...

Hello, could somebody please explain to me how 1-exp(-μt) ≤ μt and similarly (1-exp(-μt))exp(-λt) ≥ μt-μ2t2\2)(1-λt) Thanks a lot

Hello! Excuse me for my very basic understanding of math. I'll try and present my idea and problem clearly. I'd like to devise a payout structure for a tournament. 20% of the entrants will be paid. The payout will be an exponentially sloping function. The payout is in percentages that equal...

Homework Statement I have an adsorption reaction A+* \leftrightharpoons A^* Then I am to finde the rate constants and these should be given by an Arhennius relation, e.g. from left to right in the reaction: k_+ = f_+\exp(-\Delta E_a/k_bT) where the delta energy is the activation energy and...

Back to how income differences is explained in neoclassical theory, one can ask the question why GDP/capita is $5200 in Morocco and $35 500 in France. Real GDP per capita has grown at a rate of about 3.5% from 2008– 2012, GDP/capita in France grew in the same period at a rate of 1.1%...

Homework Statement I want to know the steps involved in finding the magnitude of a complex exponential function. An example of the following is shown in this picture: Homework Equations |a+jb|=sqrt(a^2+b^2) |x/y|=|x|/|y| The Attempt at a Solution For the denominator, I replaced z with e^jw...

[b]1. Homework Statement I have a sequence whereby 10000=100(1+e^(kt)+e^(2kt)+...+e^(39kt)) where k=-4.7947012×10^(-3) which was dervied from dy/dt=ky Re-arranging i get 99=1+e^(kt)+e^(2kt)+...+e^(39kt), letting e^(kt)=r I put it into the computer and i get 1.04216=r=e^-4.7947012×10^(-3)t...

Hello all, I'm having trouble showing that |e^it|=1, where i is the imaginary unit. I expanded this to |cos(t)+isin(t)| and then used the definition of the absolute value to square the inside and take the square root, but I keep getting stuck with √(cos(2t)+sin(2t)). Does anyone have any...

The sine-cosine (SC) Fourier series: $$f(x) = \frac{A_0}{2} + \sum_{j=1}^{+\infty} A_j cos(jx) + \sum_{j=1}^{+\infty} B_jsin(jx) $$ This form can also be expanded into a complex exponential (CE) Fourier series of the form: $$ f(x) = \sum_{n=-\infty}^{+\infty} C_n e^{inx} $$ and vice versa...

Homework Statement Given (e^(ix) - 1)^2 , show that it is equal to 2-2cosx Homework Equations e^ix = cosx + isinx The Attempt at a Solution After subbing in Euler identity and expanding I get: cos(x)^2+sin(x)^2-2cosx-2jsinx+2jcosxsinx + 1 after using the addtion formulas I get...

Homework Statement e^(i*2pi*1/15) is equal to ( e^(i*2pi) )^(1/15) = (1)^(1/15)=1 Why this is false? Homework Equations ((A)^(b))^c=A^(b*c)=A^(bc). Why this isn't the case for complex exponential? The Attempt at a Solution

Homework Statement Reading Hinch's book, there is a statement as follows: ... z need to be kept in the sector where exp(-z^2) ->0 as z -> infinity. Thus it's applicable to the sector |arg z|<pi/4...Homework Equations Why is this true and what is the limiting behavior of exp(x) for x in...

I have an EM problem (michelson interferometerish) where I have a term that I need to reduce. It is |1+e^{ik \Delta cos\theta}|^{2}+| e^{ik \Delta sin\theta}|^{2} I have foiled it and squared the last term but is there something that I am missing. I am multiplying it by a large matrix and...

Homework Statement Show that the exponential distribution has the memory loss property. Homework Equations f_T(t) = \frac{1}{\beta}e^{-t/\beta} The memory loss property exists if we can show that P(X>s_1+s_2|X>s_1) = P(X>s_2) Where...

Homework Statement Given f(x;λ) = cx^{2}e^{-λx} for x ≥ 0 Determine what c must be (as a function of λ) then determine the maximum likelihood estimator of λ. The Attempt at a Solution So I'm supposed to integrate this from 0 to infinity, from what i can gather. Let u = x^{2}, du...