# Questions tagged [exponential-function]

For question involving exponential functions and questions on exponential growth or decay.

5,190 questions
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### Definite integral involving modified bessel function of first kind, exponential of higher order [on hold]

Is there a solution of integral of the following form: $$\int_0^\infty e^{-x^n} J_0(x) dx$$ I have tried searching a lot but cannot find anything. Any kind of help will be appreciated.
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### Why the $e$ in $e^z$?

I am studying complex analysis, and I am learning about the complex-valued function $e^z$. But why not use another value other than $e^z$? In other words, why not use $2^z$, or $10^z$, for example? ...
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### Solve the system of equations with exponential term.

I am trying to solve this system of equations. I know the answer but I am struggling with the working. I need to solve for $m$ and $s^2$ in terms of all the other parameters. The system of equations ...
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### Exponential touch Logarithm

When I write graph for fun I found that there is some value a that make $y=a^x$ and $y=\log_a (x)$ don't touch each other and there is some value a that make $y=a^x$ and $y=\log_a (x)$ intersect each ...
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### make an exponential curve tend to a specific value

I am trying to make the following curve to exhibit an exponential decline from a given value to zero. So far, I only managed to make it go from infinite to zero.. Thus I still need to make the curve ...
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### elementary inequality involving exp and ln

Suppose $x$ and $y$ are real numbers satisfying $x\geq 0$ and $y\geq 1$. Is the following inequality true? $xy \leq e^x + y \ln (y)$ If so, is there a reference or proof?
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