# Questions tagged [exponential-function]

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

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### exponential function for pythagoras tree?

the pythagoras tree is a fractal generated by squares. for each square, two new smaller squares are constructed and connected by their corners to the original square. how do i create an exponential ...
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### Distance between exponential and first degree polynomial function

Consider the functions $$\begin{split} f(x) &= x^{2x}\\ g(x) &= 10x+2 \end{split}$$ they are defined on the interval $0 \le x \le 1.5$ I'm trying to find the maximum vertical distance ...
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### If $0<x,0<\alpha$, then $0<x^\alpha$

If $0<x,0<\alpha$, then $0<x^\alpha$ I know that If $x<y$ and $a>1$, then $a^x<a^y$ And I know the exponential laws. How can I prove it without differentation?
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### If $x,y,\alpha>0$ and $x>y$, then $x^\alpha>y^\alpha$

If $x,y,\alpha>0$ and $x>y$, then $x^\alpha>y^\alpha$ I know it's obvious when we use differnetation rule for exponential function, but I'm not allowed to. Is there any way I can show it ...
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### How to create synthetic data for a decaying curve in order to extrapolate it beyond some point? [closed]

In the following curve , I would like to extend the measurements beyond $x$=1 in order to have a better estimate of the green curve compared to red line. Note: I do not have the analytical form of the ...
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### Find one sided limit to show equivalence

I'm working on a problem that looks at growth models and I'm trying to show that the equation, $\frac{dN}{dt}$ = $aN^{\gamma}$ - $bN^{\gamma}$($\frac{N^{\gamma -1} - 1}{1 - \gamma}$) is equivalent to ...
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