Exponential Definition and 1000 Threads

Homework Statement The measure of effectiveness of a sleep deprived student studying for a test on a scale of 0 to 1 is given by the formula M(t) = ln(t^2) / 3t, where 't' is the time in hours that a student spends studying, 0 < t ≤ 4. Determine the maximum measure of effectiveness of...

Hi everyone. My final is coming up for Precalc, and I'm studying my butt off. I was really needing help with this Exponential Growth Equation to find variable t. 8.0e^(.033t) = 59.8e^(.001t) (8 times e to the .033t equals 59.8 times e to the .001t) I would greatly appreciate this...

Guys does anyone know of a technique to find the exponential of a tridiagonal symmetric matrix... Thanks in advance

Firstly, I don't get why the at term on the exponential turned positive (red arrow).. can someone explain that please? And how do I start on this? How do I split it up such that I can do it for t>0 and t=<0? Do I just integrate e^2t between -inf and 0 and integrate e^-t...

Homework Statement Find the limit as x tends to zero of: (e^-x - cos x)/2x Homework Equations lim_x->0 e^-x = 1 lim_x->0 cos x = 1 lim_x->0 sin x / x= 1 The Attempt at a Solution Hi everyone, Here's what I've done so far: (e^-x - cosx)/2x = [(e^-x)^2 - (cosx)^2] / 2x(e^-x...

Homework Statement Prove that: sinh(3x)=3sinh(x)+4sinh^{3}(x) 2. The attempt at a solution I know that: sinh(3x)=0.5(e^{3x}-e^{-3x}) and: 3sinh(x)=1.5(e^{x}-e^{-x}) But I have no idea how to rewrite 4sinh^{3}(x) in exponential form...

what does the exponential function e^x have to be multiplied by to get e^-x?

Homework Statement f(x)=f'(x) for all x in R S.T there exists a c in R such that f(x) = c exp(x) for all x Homework Equations The Attempt at a Solution By defining g = f/c, I was able to show that c= f(0) But i am also supposed to show that c Not equal to any other value I...

Homework Statement Int(-infinity to +infinity) exp[i(t^3/3 + at^2 + bt)]dt = 2pi*exp[ia(2a^2/3 - b)]*Ai(b-a^2) O.Vallee gives this formula in his book, "Airy Functions and Applications to Physics" but there are no proof of this formula. I tried to prove this formula, but I failed. Would you...

Homework Statement Given x' = Ax where A = ( 0 1 ) ( -1 0 ) Compute the matrix exponential and then find the solution such that x(0) = ( 1 ) ( 2 ) Homework Equations The Attempt at a Solution I computed the matrix exponential and obtained the matrix, e^(A) = ( cos(t)...

Hi, Does anyone knows how to solve this 2nd order non linear differential equation with exponential components? d"V/dx" = A*exp(-B*V)-C*exp(B*V) where A, B, C are constants. Thanks

Homework Statement L(t)=15(0.5^(t/26)) Find the rate of L, when t=60 Homework Equations The Attempt at a Solution L'(t) = (15/26)(1/2)^(t/26)ln(1/2) L'(60)=(15/26)(1/2)^(60/26)ln(1/2) = -0.08 Did I do this right? If I did it wrong, please say where, I am having great...

Homework Statement Given the matrix: A=[-2 0 0;4 -2 0;1 0 -2], find e^AT. I found the eigenvalues to be -2,-2,-2. How do I solve this problem with 3 identical eigenvalues? Do I cube to matrix after plugging in my eigenvalue -2 and then solve it that way? After plugging in the...

Homework Statement Solve the equation e^x+10e^-x=7 Homework Equations Logarithm rules and the natural logarithm The Attempt at a Solution Not really a calculus question but one I'm lost on nevertheless. I don't know how to go about solving this question at all. My first attempt...

Homework Statement Species A doubles every 2 hours and initially there are 6 grams. Species B doubles every 5 hours and initially there are 14 grams. Homework Equations The Attempt at a Solution I've tried graphing this, but I don't think I have the right equations down. I don't...

(x^2).e^(-2a(x^2)) how would i integrate this? By parts? If so using |udv = uv - |vdu (hope that's right) would i let u = x^2 and dv = e^(-2a(x^2)) ? but how do I integrate dv = e^(-2a(x^2)) to find v ? any help appreciated :)

Homework Statement The actual problem shows a graph however I can state all the information. The graph is of a sinusiodal waveform where the amplitude is decaying exponentially. The formula for the graph is given by the equation: T = Ae-Ktsin(wt + ø) The question is to find A,K,w and ø...

Homework Statement I'm trying to verify the Fourier transform but am getting stuck on the integration. Here is the pair: f(x) = e^{-ax^2} \hat{f}(k) = \frac{1}{\sqrt{2a}}e^{-k^2/4a} a>0 Homework Equations I know that \hat{f}(k)=\int_{-\infty}^{\infty}f(x)e^{ikx}dx The Attempt at a...

Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate: 1: \frac{e^3^x}{\ln x} I just don't know how to put it together... I know that e^3^x is 3e^3^x, and I know that you can't different \ln x, so I don't know what to do from there...

Homework Statement 3^x + x = 4 solve for x. Homework Equations I'm thinking of using the logarithm laws. log(a.b) = log a + logb log(a/b) = log a - log b log(a^b) = bloga The Attempt at a Solution Well if I isolate the exponential 3^x = 4-x take logs on both sides xlog3 = log(4-x) I...

Homework Statement If spraying of grasshoppers with 800kg/km^2 of a certain insecticide will kill 40% of these insects, how much insecticide is needed to kill 98% of the grasshoppers? (assume exponential relationship) Homework Equations \intdP/dt=\intkp lnP=kt+c e^(kt+c)=PThe Attempt at a...

Homework Statement The population of a country is growing exponentially. The population in millions was 120 in 1970 and 150 in 1980. (a) What is the population t years after 1970? (b) How long does it take the population to double? (c) When will the population be 400 million...

Homework Statement a. Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/dz, the variation of...

what is e^{jw\infty} ?

Suppose I have several exponentially distributed random variables, each of them representing the probability that some particular event occurs within some amount of time. I can't seem to come up with any intuition as to how to combine those density functions (or distribution functions) to...

I am looking a formula to compute the derivitative of e^{a x^2} with respect to x n times, where a is a constant. \frac{d^n}{dx^n}e^{a x^2} I am going to find the result of above derivitative when x -> 0.

Homework Statement The time between calls to a corporate office is exponentially distributed with a mean of 10 minutes. What is the probability that there are more than three calls in one-half hour? Homework Equations F(x) = P(X <= x) = 1 - e^-(lamba*x) The Attempt at a Solution...

Homework Statement 1. \int^{\infty}_{-\infty}e^{-ax^2 - bx^{\frac{5}{2}}}dx 2. \int^{\infty}_{-\infty}x^ne^{-ax^2 - bx^{\frac{5}{2}}}dx (n is integer) Homework Equations Does anyone can give me the integral in the closed form or introduce any useful references? Thank you.

Homework Statement Find the exponential function that passes through the points (2, 1) and (5, 7). Homework Equations y= Ce^ (kt) The Attempt at a Solution I can only get as far as substituting in 2 for t and 1 for y, then I'm completely stuck.

Homework Statement A curve passes through the point (0,6) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? Homework Equations Y=Yoe^kx is a solution of (dy/dx)=ky, where k is constant The Attempt...

In general what do you do when some kind of data is missing from some data that follows exponential distribution. For example, say 3 observations are made by an instrument where x1=5, x2=3, but for x3 the instrument can not give a specific answer because it can't measure past 10. So the only...

Homework Statement X is exponentially distributed. 3 observations are made by an instrument that reports x1=5, x2=3, but x3 is too large for the instrument to measure and it reports only that x3 > 20 . (The largest value the instrument can measure is 10) a)What is the likelihood function...

Homework Statement Solve the equation: (x+xy^{2})dx + e^{x^{2}}y dy =0 Homework Equations n/a The Attempt at a Solution i) xdx(1+y^{2}) = -e^{x^{2}}y dy (multiply both sides by 2 to prepare for integration: ii) \frac{-2xdx}{e^{x^{2}}}= \frac{2y dy}{1+y^{2}} integrate and get: iii)...

¡¡get matrix exponential Please! Homework Statement I have a exam and i don't know how get matrix exponential: | 2*t t| | 3*t -t| it is a 2x2 matrix. where 't' is not a constant ,it is a variable somehere could help me,please. Homework Equations The Attempt at a Solution...

Homework Statement This isn't a problem, I'm just obsessed with analyzing a trig/exp equation algebraically instead of with a calculator. 8*sin(t) - 16*cos(t) = 9*exp(-t/2) Homework Equations See part (1.) above... The Attempt at a Solution I tried converting the exp part...

Can a convenient value for a be found without resorting to substituting numerical values for h in this expression? EDIT: I am trying to indicate, "as h approaches zero". EDIT: neither of the formattings worked; hopefully someone understands what I am asking...

Homework Statement I'm new to integration, and was attempting the integral of ex with respect to x. Homework Equations \intex dx The Attempt at a Solution Should I keep it in the format y=ex so that I use this in the calculation of the area? Or should I convert to ln y? I got stuck...

Hi! I want to know how to intergrat e^(-(x^2)/2) . Someone told me to use the intergration of e^x= 1+ x + (x^2) /2!+ ...(X^n)/n! ... is that sounds right?? and if it is i got pi as an answer for e^(-(x^2)/2) , is that the right answer?

Homework Statement Determine the period in which y = Cekt changes by a factor of q. I have no idea what it is asking.. find t when k=q?

Theorem Let A be a square matrix nXn then exp(At) can be written as exp(At)=\alpha_{n-1}A^{n-1}t^{n-1} + \alpha_{n-2}A^{n-2}t^{n-2} + ... + \alpha_1At + \alpha_0 I where \alpha_0 , \alpha_1 , ... , \alpha_{n-1} are functions of t. Let define r(\lambda)=\alpha_{n-1}\lambda^{n-1} +...

Hi, I'm trying to solve the following: f(x) = \int^\infty_{-\infty}ce^{yx-y^2/2} dy where c is a constant My only idea thus far was that since it is an even function, the expression can be simplified to: = 2c\int^\infty_0 e^{y(x-{1/2}y)} dy but I'm stuck here. Anyone know how to do...

Homework Statement Show that (ez)*=ez* note: * is the conjugate Homework Equations The Attempt at a Solution So I wasn't sure what form to put this in...either in exponential reiѲ or cos Ѳ + isin Ѳ...Either way, I think I'm just making it too easy... Please help!

Homework Statement What is the derivative of ex3? also what is the derivative of (ln1/x)2Homework Equations The Attempt at a Solution is it 3x2e3x2? 2(ln1/x)(x)?

Hello, In a paper, the authors defined an exponential Random Variable (RV) as X_1 \mbox{~EXP}(\lambda) where \lambda is the hazard rate. What will be the distribution of this RV: f_{X_1}(x)=\lambda e^{-\lambda x} or f_{X_1}(x)=\frac{1}{\lambda} e^{-\frac{x}{\lambda}} Thanks in advance.

Homework Statement The problem asks to graph tangent lines to the given function y = (ln(x)/x, and gives the points (1,0) and (e, 1/e) Homework Equations The Attempt at a Solution I got the answer by taking the derivative and finding the slope, and at the point (e,1/e) the...

Homework Statement Hello. I'm afraid it's quite a simple and unexciting problem I have. Basically, I can't remember how to rearrange the equation for an exponential curve: The capacitor has a capacitance of 0.63 mF and the resistance in the discharge circuit is 2.4 kΩ. (i) Calculate...

1. It is estimated that x years from now the value of an acre of farmland will be increasing at the rate of \frac{0.4x^3}{sqrt(0.2x^4+8000)} dollars per year. If the land is worth 500 per acre, how much will it be worth in 10 years? 2. Use integral Since the the function of money...

Homework Statement The distance between major cracks in the highway follows an exponential distribution with a mean of 5 miles. What is the probability that there are two major cracks in a 10 mile stretch of the highway? Homework Equations exponential dist: f(x) = Le(-Lx) where L...

I have seen the following identity used. Exp[iw/2]-Exp[iw/2]=Exp[iw]-1 I can't find this in any book and I can't prove it myself. The left side equals 2isin(w/2) The right side equals cos(w)+isin(w)-1 On the face of it, that seems to make the identity absurd How can one go about proving...

Homework Statement Consider a horizontal slab of air whose thickness(height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for Dp/dz, the variation of pressure...