Exponential Definition and 1000 Threads

Hi I'm self-teaching calculus and I'm looking at exponential growth and decay. The differential equation for relationships like these if this was related to time is dP/dt = -kP i.e. the rate of change in P with time decreases at a rate which is proportional to the amount of P present. I can...

Homework Statement - The following table gives the population of a city over time: Homework Equations I know this equation: y = a(b)x and exponential growth: b = 1 + growth rate and b = 1 - decay rate The Attempt at a Solution I know from back in chapter 2 that first...

Homework Statement I have problem solving an integral equation of the form Homework Equations \int_{0}^{\infty}(a\Lambda^2/(\Gamma(\gamma-\Lambda)^2))exp(\Lambda\gamma/(\Gamma(\gamma-\Lambda))-(\gamma-b)/c)d\gamma The Attempt at a Solution I have tried to solve it by...

Sorry if this might be in the wrong section, but I wanted someone's opinion on the formation of rust. Do you think that the rate of formation of rust on iron/steel is an exponential growth?... --- Also, some extra. I'm doing an EEI on rusting - basically, I'm trying to find the best...

Hi there,Struggling with this problem, anyone know how this might be solved? (e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152) and solve for r Ans: r~2.90% Would really appreciate it!

Hello, How can I find the limit of x^{k}\mathrm{e}^{-ax^n} for x\to +\infty. a,k,n are positive reals. I even have troubles solving it for k=1, a=1, n=2. Any hint?

Hi everyone, here is this integral I can't find solution: \int_0^\infty \frac{x e^{-x}}{A+Bx} dx A and B are constants. I'm going crazy, I don't think there is even an analytical solution.

Homework Statement Hi, I need to find the spectrum of the following function: i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]Homework Equations the Fourier Transform would be: \int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi...

Hi, I am trying to find an analytic solution to the following double integral...

Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution

Hi, Does anyone know of an analytic solution for the integral \int_{0}^{\pi}\sin\theta\exp\left(a\sin^{2}\theta+b\sin\theta\right)d\theta Thanks.

Hello, for continuous compouding (in the exponential growth and decay) the function for interest after t years is: A(t) = A0*e^rt A0 should be read A at time 0 in the book, they say when you differentiate this function this is what you get dA/dt = r*A0*e^rt = rA(t) I don't see...

Homework Statement Derive an equation of the form y=ax^b to model the given data: (35, 0.01) (28, 0.03) (20, 0.1) (15, 0.3) (11, 1) (9,3) (6, 10) (4.5, 30) Homework Equations Well, I know the answer is y = (7790 +/- 1246)x^(-3.698+/-0.1036) because that's what LoggerPro spits out, but...

I forgot how to derive the mean of exponential random variables follow the chi square distribution with degree freedom 2n. Don't know where I got it wrong. Anyone have a clue how to do it? Thanks

Homework Statement a.) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean u = 1000, find the probablity that both of the lamp's bulbs fail within 1000 hours...

I have a density function: f(t) = L * e-L(t-t0) * u(t-t0) where u(t) is the unit step function. And I have a column vector X, which is randomly chosen samples from f(t): X = [x1 x2 ... xn]T How can I estimate the unknown values t0 and L from this X vector?

This is part of double integral. I just can't seem to figure out what I'm doing wrong. The inner integral comes out to be: \int_0^\infty{e^{-xy}dy} I emailed my teacher to help me through it, and he says this should integrate down to 1/X but I can't seem to figure out how. I'm no good...

Homework Statement ex / (1 + ex)

Homework Statement Solve the following equations using simultaneous equations Homework Equations 32x\times23y=17 4x\times5y=37 Appologies for the bad equation set-up. The large 'x' is a multiplication sign. The Attempt at a Solution My attempt was to divide both of the...

Homework Statement A particular species of mollusk is distributed according to a Poisson process with an unknown density of lambda per cubic meter of water. A sensor is constructed that can detect these species that are within 4 m, and n readings are collected over a year to try and measure...

Homework Statement IF X has an exponential distribution with parameter \lambda, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median. Homework Equations X.exp(\lambda)=\lambda e^{-\lambda x} for x>0 p=F(\eta (p)) =...

Homework Statement A tissue culture grows until it has an area of 9 cm^2. Let A(t) be the area of the tissue at time t. A model of the growth rate is that: A'(t) = k*(sqrt(A(t)) * (9-A(t)) a. Without solving the equation, show that the maximum rate of growth occurs at any time when...

e ^ (-2 ln |x + 1|) = e ^ ln [1 / (x + 1)^2] how can this happen? can anyone explain to me the process of this equation..

Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)

Homework Statement To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the number of units x ordered. The discount decreases the price at a rate of $0.01 per unit ordered. The price per unit for a...

Find the real part of the complex number: (1-12i)e^{-2+4i} I know that z = a + ib can be rewritten as z = |z|e^{i\theta} but that doesn't help because the coefficient of the e is not a scalar value, rather a complex number. Thanks Tom

Say we have a decay of the form A e^{-a x} + B e^{-b x}. I haven't had much luck trying to calculate the half-life of such a decay (I'm not sure it's possible, analytically), i.e. solve A e^{-a x} + B e^{-b x} = \frac{A+B}{2}. However, if that's not possible, I'm wondering whether...

I have been stuck at this calculation. There are two exponential distributions X and Y with mean 6 and 3 respectively. We need to find E[y-x|y>x] I keep getting it negative, which is clearly wrong. Anybody wants to try it?

My friend just came to me with this problem: e^x + e^-x = 4 I aced precalc, and I still have no idea where to start on this one. I've factored, natural logged, factored and then natural logged... and I keep running into dead ends. My graphing calculator puts the answer at +/-1.3169 or...

Homework Statement P(r) = 1-(2r2+2r+1)e-2r i know that p(r) is just the derivative of P(r) to find the median i would just integrate from o to r and set that equal to .5 but when you integrate youre just going back to P(r) from 0 to r so i get 1-(2r2+2r+1)e-2r = .5 how would...

Homework Statement lim_{x->0} (1+ sin5x)^{cotx} Homework Equations that's the problem.. I don't know :s The Attempt at a Solution can't think of any theorems or any methods I could use here.. what should I do? thank you

Homework Statement Trying to solve for K: ln(1-4k)=-6k Homework Equations The Attempt at a Solution I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.

So I was playing around with logarithmic & exponential amplifiers in my lab class. I was looking at the following equations: http://upload.wikimedia.org/math/7/7/6/77663157d5b97ceb2e3edac5f587a620.png and http://upload.wikimedia.org/math/b/3/c/b3c569c85552561e41dec916f6e8ebe8.png...

Homework Statement Hello i am doing a cooling experiment and i want to know the following: y=28.49e^(-0.03890*800) +26.51 (note the 26.51) is not part of the exponential. What is y? and I was wondering whether this would go ever go through the x axis? Thanks people! Homework...

Homework Statement Find the second derivative of: e^{ax} and e^{-ax} Homework Equations The Attempt at a Solution The book that I am using seems to have been very vague on how to take the derivatives of exponential functions. I am aware that: \frac {d(e^{x})}...

How would you integrate something like xe(x^2) by using a substitution like u=x^2

Exponential Equation! -Stuck!- 1. 32y+3 = 3y+5 The Attempt at a Solution 2y + 3 = y+5 2y = y+2 I really don't think I am doing this right, I am trying to find the value of Y. the answer is 2 but I don't know how to come up with the answer.

Homework Statement We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for...

Homework Statement how would you integrate, int (-ik - 2ax)*exp(-2ax^2) dx with limits infinity - infinity Homework Equations i think i can use the result int exp(-x^2) dx = sqrt (pi). But I am stumped. The Attempt at a Solution i thought about multiplying it out int...

Hello! I found on this webpage: http://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/costate.pdf page 1, on the bottom that e^{\phi^* a } f(a^{\dagger} , a ) = f(a^{\dagger} + \phi^*, a) e^{\phi^* a } I have tried to prove this, writing both as taylor series, but the problem is to...

Homework Statement Let z=x+iy prove that Exp[z1]*Exp[z2]=Exp[z1+z2] Homework Equations Binomial thm (x+y)^n=Sum[Bin[n,k]*x^n-k*y^k,{k,1,n}] The Attempt at a Solution I have no idea about this question... Please give me some help.

I'm just a neuroscientist, so forgive me if the answer to this question is either obvious, or the answer is that it is impossible, obviously. Basically, this image should outline the question clearly http://img713.imageshack.us/img713/2569/mathsissuefixedyxs.gif (And Y0 is always 1)Also, I...

I am reading conflicting interpretation of the Hubble constant in the exponentially expanding accelerating universe. Some say the Hubble constant is continuing to decrease; while others say Hubble constant is now unchanging and has become truly a constant. Which is correct?

can someone please explain the difference. Graphically and mathematically it is easy to see they are inverses. But I see certain scales like the Richter scale that seem to increase exponentially, but are labeled as logarithmic scales. for example, on the richter scale with each increase in...

Homework Statement I am working on a problem, and there is a small step I need help on: I have the expression eab, where a is a constant, and b is a variable. I need to separate a and b so I can pull out the expression b from an integral expression. Is there any exponent law or manipulation...

Can someone give me a starter hint for this problem? Brain's not working at full speed... 3^(2x) - 2*3^(x+5) + 3^10 = 0 Thanks

Homework Statement Homework Equations The Attempt at a Solution Ive numbered the solution steps, the ones that are giving me trouble are from 1 to 2 and from 3 to 4 From 1 to 2 i don't understand how there can be an exp(x) term taken out of the bracket and still be in the...

hi guys I need The proof from definition of the derivative for exponential and log Fn can somebody help me !

Homework Statement Briefly, the question asks to prove how the interference of 2 electrons (travelling in opposite directions as 1-D waves) would affect the probability of finding each electron in free space. My issue has to do with the first step in the solution. Homework Equations...