Exponential Definition and 1000 Threads

Homework Statement The total amount of oil in a well is 24000 barrels. The present rate of consumption is 100 barrels per year. How long will the gas supply last if the present yearly rate of consumption increases by 1% per year? Homework Equations We can use the approximation (1+x)^i =...

In class, my teacher was motivating Schrodinger's Equation, but there is one step that I do not understand or even have intuition for. I'll give the argument leading up to the step I do not understand for context. Let \hat{U}(t) be the operator that gives the wave function after time t, given...

Homework Statement This is a subset of a larger problem I'm working on, but once I get over this hang up I should be good to go. I have a set of measurements x_n that are exponentially distributed p(x_n|t)=e^{-(x_n-t)} I_{[x_n \ge t]} and I know that t is exponentially distributed as...

Homework Statement Forgive the awkward title, it was hard to think how to describe the problem in such a short space. I'm following the proof of Proposition 1.2 of Nakahara's "Geometry, Topology and Physics", and the following commutation relation has been established: \partial_x^n e^{ikx} =...

Homework Statement A body is found at 2:00pm at a temperature of 26°C, with a surrounding temperature of 18°C. Two hours later the temperature of the body is 21°C, when did the body die? T=Ae^(kt)+Ts where T is the temperature of the body A is the initial temperature k is a constant t...

Homework Statement \vec{N} = \frac{1}{\tau}(\int_0^\infty exp(t' \textbf{T}) dt') \vec{n}_0 Show that \vec{N} = -\frac{\textbf{T}^{-1}}{\tau}\vec{n}_0 where \textbf{T}^{-1} is the inverse matrix of \textbf{T}. It is part of a small project called Gambler's Ruin in which we investigate...

If the concentration of caffeine in a system at any given time is given by the equation y(t)=De^-kt where dy/dt=-kt is the clearence rate (re-arranged and integrated to form the above equation) and the concentration of caffeine in the system at t=0 is D, then calculate k if: After one hour...

This is A and B my friend is telling me that Co is actually 0 and I am getting 1/2 and i don't see exactly what I am doing wrong if i indeed am doing something wrong hopefully someone here can check this out and let me know exactly where i went wrong.. Thanks

Homework Statement \Psi(x,t) = \int^{\infty}_{-\infty} C(p)\Psi_{p}(x,t) dp is a solution to the Schroedinger equation for a free particle, where \Psi_{p}(x,t) = Ae^{i(px-Ept)/\hbar}. For the case C(p) = e^{-(p-p_{0})^{2}/\sigma} where \sigma is a real constant, compute the wavefunction...

Homework Statement Suppose that X has an exponential distribution with mean μ. Find the probability that x lies within one standard deviation of its mean, that is find P(μ-σ≤X≤μ+σ) Homework Equations The Attempt at a Solution If I'm not mistaken the standard deviation is equal...

Jordan from Facebook writes: Got the first one right, don't know exactly what it's asking for in the 2nd part(I missed the class that we went over these types of problems) thanks!

What is |exp (z^n)| less than if |z| < 1? I'm thinking it's e but I'm having a brain freeze at the moment! Thanks for any help guys.

How do i derivate e^e^x (I don't know how to type it on latex but here you can se what i mean e^e^x - Wolfram|Alpha Results basicly don't know how I shall think

In class we recently learned that for a linear operator T: V \rightarrow V and function g(t) = a_0 + a_1t + \dots + a_nt^n one can define the operator g(T) = a_0I + a_1T + \dots + a_nT^n (where I is the identity transformation). We also recently learned about the exponential of a matrix. My...

Homework Statement I have developed an equations for calculating some pollutant concentration as a function of x and y. I'm trying to simplify the problem so that I can write the equation for wp as a function of x. All variables except x and wp are known. Homework Equations...

Homework Statement Use exponential notation to write (√3-i)(1+i√3) in the form a+ib. Homework Equations The Attempt at a Solution Let (√3-i) = z1 r1=|z1|=√((√3)2-i2) =√(3-1) =√2 Therefore, √3=√2cosθ and -1=√2sinθ cosθ = √3/√2 and sinθ = -1/√2 θ= arcsin(-1/√2) θ= -∏/4...

Homework Statement I'm trying to find the value of a variable which happens to be an exponent. Homework Equations 230,000=1500\frac{(1+.00077)^n-1}{.00077} I believe I need to use logarithms to get to my answer, but I've reviewed logarithm rules and I'm stuck. The Attempt at a...

Having an issue with applying logarithm rules. I'm trying to find the value of an exponent in an equation of the form: A=B\frac{(1+x)^n-1}{x} I have reviewed logarithm rules and cannot get to the answer, n, which is the only unkown variable in the equation. I've divided A by B, but am stuck at...

Hi! I was wondering why it is possible to write any proper orthochronous Lorentz transformation as an exponential of an element of its Lie-Algebra, i.e., \Lambda = \exp(X), where \Lambda \in SO^{+}(1,3) and X is an element of the Lie Algebra. I know that in case for compact...

Dear members, see attached pdf file.Can you help me to prove this formulas. Thank you Belgium 12 This is not homework.I'm 68 and retired.

Homework Statement A 44 gallon barrel of oil develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at a given time t. Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel. a...

Hello all, I am searching for an analytic solution to an integral of the following form: I[q',k\rho\,]=\frac{1}{\pi}\int_{0}^{2\pi}e^{jq'(\phi-\phi_0)}e^{-jk\rho\sin(\phi-\phi_0)}d\phi In this equation, q' is real and k\rho is real and positive. Also, the following integral is closely...

This whole chapter has been tripping me. My professor made-up another way of doing this, which I'm having a hard time understanding. He's a really intelligent guy(even other professors say it) so he can do this, but I'm having a hard time understanding his way. I went to tutoring today, they...

I need help with understanding two questions: 1. (2x+2)2 The answer I got was: 22x+2x++4, but according to the answers that is wrong. Can any explain why? 2. 84x/32x I simplified this to become (84/32)x, but I don't know how to go from there... The answer is apparently 27x, but I don't...

determine if the following congruence has an integer solution: 5x + 4 congruent to 5 (mod 100) The only way I could envision this working is by trying all of the remainder values of 100, but I don't think that is the way to go considering there is so many. I tried to figure out an...

I'm reviewing math material for the EIT exam, I'm going over math concepts that should be pretty basic but I feel like there are gaps in my understanding. I understand how we can use rectangular coordinates and complex numbers to find a point on the complex plane. It would follow logically...

Homework Statement The copy of the question is in the image attached. I don't have a graphing calculator, and so am not sure how to determine the equation of the exponential function. Homework Equations y = a^x The Attempt at a Solution I made a scatter plot off of an online...

Q A cold yam is plaveedd in a hot oven. Newton's Law of Heating tells us that the difference between the oven's temperature and the yam's temperature decays exponentially with time. The yam's temperature is initially 0 deg F, the oven's temp is 300 deg F, and the temp difference decreases by 3%...

The number of bacteria in a culture is given by B(t) = 40e0.6t, where t is the time in days. How many bacteria are there after 2 days? I substituted t = 2, and got this: 2B = 40e1.2 which I simplified to become this B = 66.4 days Apparently this answer is wrong though, can someone explain why?

A pdf is of the exponential family if it can be written $ f(x|\theta)=h(x)c(\theta)exp(\sum_{i=1}^{k}{w_{i}(\theta)t_{i}(x))}$ with $\theta$ a finite parameter vector, $c(\theta)>0$, all functions are over the reals, and only $h(x)$ is possibly constant. I would like to show the binomial...

Homework Statement Let T be an exponential random variable with parameter λ; let W be a random variable independent of T , which is ±1 with probability 1/2 each; and let X = WT. Show that the density of X is: f_{x}(x)=(\lambda/2)e^{-(\lambda)\left|x\right|} Homework Equations Density...

1. Let's say that at the end of 2010, the population of Athens was 100,000. Let's also say that the relative growth rate of the population was 2% per year. What's the population at t = 0.5 years after the end of 2010? 2. To solve this sort of problem, I thought I'd have to use: y= A(1+b)t A is...

Homework Statement exponential integration formula ∫a^{u} du = \frac {a^{u}}{ln(a)} +c ∫ \left(\frac{2}{3}\right)^{x} dx Homework Equations \frac{}{} The Attempt at a Solution ∫ \left(\frac{2}{3}\right)^{x} dx = \frac{\left(2/3 \right)^{x}}{ln(2)/ln(3)} <<< this is my answer ?= -...

Hello! Could someone please help me answer this question, and explain how you answered it? 1. (x1/2 + x-1/2)2​Thank you!

Homework Statement The total claim for a health insurance policy follows a distribution with density function f(x) = (1/1000)e^{-x/1000}, x>0 The premium for the policy is set at 100 over the expected total claim amount. If 100 policies are sold, what is the approximate probability that...

Hey Guys, From my understanding, the linear doubling time of a reactor is the time which the fissile nuclides in the reactor core double under a constant flux. The exponential doubling time of a reactor is the time it takes for the fissile material in a core to double if you take each atom...

Here is Abby's question: Here is a link to the original question: Differential Equations time constant problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I recently struck a question that I have not been able to find an answer to. I feel like I'm missing something obvious, so I've come here for help. The derivative of a^{x} is a^{x}lna. The explanation that Stewart 5e gives is: \frac{d}{dx}a^{x} = \frac{d}{dx}e^{(lna)x} =...

Homework Statement Find the equation of the tangent line to the graph of y = lnx2 at the point (2, ln4) Homework Equations The Attempt at a Solution y' = (lnx2)' y' = 2lnx y' = (2)(lnx)' + (lnx)(2)' y' = 2/x Mtan/(2,ln4) = 2/2 = 1 Equation of tan line: y - ln4 = 1(x-2) y = x - 2 + ln4

Homework Statement PROBLEM 1 Find slope of tangent line at (1,0) g(x) = x2lnx Solution: g'(x) = (x2lnx)' g'(x) = x2[1/x . (x)'] g'(x) = x2 . 1/x g'(x) = x M tan/(1,0) = 0 PROBLEM 2 Use implicit differentiation: yex+ y2 = 7lny - x3 Solution: (ex)(y') + 2y(y') - 7(y'/y) = -ye - 3x2...

Homework Statement 2^x + 2^(4-x) > 17 2.The attempt at a solution I factorized for 2^(-x) so I have 2^(-x) * (16 + 2^(2x)) > 17 but I don't know what to do after... could you help me ? thanks

Homework Statement Positron Emission Tomography (PET) scanners frequently operate us- ing the radioactive isotope 18F, which has a half life of about two hours. The isotope is incorporated into a drug, half of which is excreted by the body every two hours. How long will it take before the...

Homework Statement 5^( \sqrt(x) ) + 5 * 5^(- \sqrt(x) ) = 25 + 1/5 2. The attempt at a solution I have thought to transform 5^ (-\sqrt(x) ) in (1/5)^(\sqrt(x) ) but I don't know how to solve then... could you help me ? thank you

The Information Systems Audit and Control Association surveyed office workers to learn about the anticipated usage of office computers for holiday shopping. Assume that the number of hours a worker spends doing holiday shopping on an office computer follows an exponential distribution. a) The...

I have the integral \int_{-\infty}^{\infty}dx \int_{-\infty}^{\infty}dy e^{-\xi \vert x-y\vert}e^{-x^2}e^{-y^2} where \xi is a constant. I would like to transform by some change of variables in the form \int_{-\infty}^{\infty}dx F(x) \int_{-\infty}^{\infty}dy G(y) the problem is...

Homework Statement k is a real number and f_{k}(t)=e^{t}-1-t-k\frac{x^{2}}{2} 1- Show that : (\forall x\epsilon\mathbb{R}):0\leq e^{x}-1-x 2- Show that : (\forall x>0)(\exists k\epsilon\mathbb{R}^{+})(\exists d\epsilon[0,x]):f(x)=f''(d)=0 3-Conclude that (\forall...

Homework Statement Find extrema and points of inflection (then graph it). f(x) = x2e-x Homework Equations The Attempt at a Solution So, for f'(x) = xe-x(2-x) Critical point(s): f'(x) = 0 2-x = 0 x= 2 I have a question before continuing. Will my critical point include 0 besides 2? I...

Homework Statement ∫(0 to 2) ∫(2x to 4) [e^(-y^2)] dydx This was a question given for a multivariable class exam a couple years ago, and we don't ever learn about the exponential integral in that class. Homework Equations We know how to go about solving this, BUT... The Attempt at...

$\int x (5^{-x^2})dx= -\frac{1}{2} \int 5^{-x^{2}}(-2x)dx$ how is $\frac{1}{2}$ in front of the $\int$ derived

Homework Statement 52x - 3(5x) = 10 Homework Equations The Attempt at a Solution log 52x - log 3(5x) = log 10 2x log 5 - log 3 - x log 5 = log 10 x log 5 = log 10 + log 3 x = (log 10 + log 3)/log 5 putting this in my calculator I get 2.11 by inspection I can tell that the...