# exponential

1. ### Optimization Problem with Exponential Form (double terms)

Hello, Could anybody help me with this optimization problem? I want to minimize sum(s=1,S) a_s * exp(b_s*x_s) + c_s * exp(d_s*x_s) subject to the constraint: sum(s=1,S) x_s = A I am supposed to find x_s which makes the statement minimized. a_s, b_s, c_s, d_s, and A values are constants in...
2. ### Exponential tetration

Here is a page for those who want to know about exponential-tetration . https://en.m.wikipedia.org/wiki/Tetration
3. ### Exponential equation

Check whether I solved the equation correctly for real numbers : x^{\frac{1}{x} } =-1 \; , x-integer and by domain x\neq 0. By natural logarithm to both sides : \frac{1}{x} \ln (x)=\ln(-1)=i\pi . x=e^{ix\pi }=\cos (x\pi )+i\sin(x\pi)=\cos(x\pi)=(-1)^{x}. x=(-1)^{x} \; and if solution...
4. ### Exponential function

Just graphed the function f(x)=x^x using a graphing calculator . Does the function makes sense for x=-1 ? By the graphing calculator the negative values of x are not included. For x=-1 , f(x)=-1 . Why negative values are avoided ?
5. ### Request for help with tricky Riccati DE with exponential terms.

Hi all, I am developing a model that requires me to derive the solution of a rather tricky Riccati DE, and I am having a devil of a time with it and am beginning to wonder if there is even a closed-form solution. Anyhow, the equation is \frac{dE}{dt} = cB_{t} + bE_{t} + aE_{t}^{2}...
6. ### Exponential equation problem

I have the following equation 2^x+2^(-x)=3 4^x+4^(-x)=? The solution is 7, but I don't know how to reach that answer. Can anyone help me?
7. ### Exponential growth question for the mathematicians who love family trees

Here's something for the mathematicians that are also genealogists, since those subjects get intertwined a lot. I put this under Number Theory because of the exponential growth that comes with family trees. Anyway, I'm working on my mum's ancestry - one of her 16 great-great-grandparents was...
8. ### Directional derivative of exponential of a function

I have a trouble of a directional derivative of a function : for a function f and a tangent vector field X of a manifold M, we have X(f)=âˆ‡_{X}f=<âˆ‡f,X> From this above formula, is it true that : X(e^{-f})=<âˆ‡e^{-f},X>=<e^{-f}âˆ‡(-f),X>=-e^{-f}<âˆ‡f,X> If it not...
9. ### Problem with an exponential equation

Hi, I need help with this exponential equation. Normally, I would use 3^x as a substitution, but the 3^(-x) is kinda confusing me. How am I supposed to solve this? Thanks. 9*3^x+3^(-x)=10 So I figured it out: 1/3^x = 3^(-x)
10. ### One exponential equation

Equation 81^\sin^2 x+81^\cos^2 x=30 can easy be solved by substitution 81^\sin^2 x=t What about equation 81^\sin2x+81^\cos2x=30? I think it doesn't have real solutions.
11. ### Challenging Derivatives of Exponential and Sinusoidal Functions task question

A common brand contains 30 mg of codeine. Since it is physically addictive and has other unwanted side effects, it is important to avoid an overdose while helping to relieve pain symptoms such as those caused by a headache. Samples of blood were taken at regular time intervals from a patient who...
12. ### Exponential equation

I don't understand how to pass from -0.04t = ln (2/3) to t= -25 X ln (2/3) Thank you in advance
13. ### Posterior Distribution from Beta Density with Exponential Prior

Let $X_1,...,X_n$ be iid random variables with a common density function given by: $f(x|\theta)=\theta x^{\theta-1}$ for $x\in[0,1]$ and $\theta>0$. Put a prior distribution on $\theta$ which is $EXP(2)$, where $2$ is the mean of the exponential distribution. Obtain the posterior...
14. ### exponential limit

finding \displaystyle \lim_{n\rightarrow \infty}\frac{a^n}{n!}, a>0
15. ### Exponential identity

0 is the additive identity; i.e. 0+R=R 1 is the multiplicative identity; i.e. 1*R=R 0 is an "exponential inverse"; i.e. R^0=1 for Râ‰ 0 1 is an "exponential identity"; i.e. R^1=R 2 is a "universal identity"; i.e. 2+2=2*2=2^2
16. ### exponential equation

11^n =11n \; \; for n\in N Use Number Theory theorems or approximations Post your method (just posting for curiosity); I'll post my idea too.
17. ### exponential growth

In 1923, koalas were introduced to Kangaroo Island. In 1996, the population was 5000. By 2005, the population had grown to 27000, prompting a debate on how to control their growth and avoid koalas dying of starvation. Assuming exponential growth, find the continuous rate of growth of the koala...
18. ### Exponential Diophantine Equations

Hi, Solve : 1/ n,k\in \mathbb{N}, 29+2^n=3^k 2/ n,k\in \mathbb{N}, 1+2^n=3^k 3/ a,b,c\in \mathbb{N}, 2^a+3^b=5^c Cordially.
19. ### Question on exponential functions

I am taking an online college algebra class and we just started exponential and logarithmic functions. Our instructor is always urging us to think about the math and not just plug numbers into a formula and spit out answers, so I am and I have questions! If I were to plot a basic...
20. ### Question on exponential functions

So, I'm taking an online class for college algebra and we just started exponential and logarithmic functions. Our instructor urges us to think about the math and not just learn formulas and to plug in numbers, sooooo I did just that and now I have a question. In particular, if I were to...