1
vote
1answer
51 views

Rewriting in $y=A_0\cdot e^{at}$

How do you rewrite $y = −8(1.589)^{t − 3}$ in $y=A_0e^{at}$ form for appropriate constants $A_0$ and $a?$ For other problems I took the $\ln$ of the number inside the parenthesis. So for example I ...
1
vote
1answer
47 views

Outputting inequality with $e^x$

I many books I can find inequality which estimates $e$: $$\left(1+\frac{1}{n}\right)^n \lt e \lt \left(1+\frac{1}{n}\right)^{n+1}$$ I am wondering if correct is also to write: ...
0
votes
2answers
67 views

Asymtptotic limit of $e^x$ [closed]

I am looking for functions $A,B$ such that $$ A < e^x < B.$$ $A,B$ should be as close to $e^x$ as possible. I was trying to find something, but all I found was very distant. Can someone suggest ...
1
vote
1answer
81 views

Practical significance of $e$ [duplicate]

We know, for example, the constant $\pi$ is the perimeter of a circle with diameter $1$ unit. In the similar manner how would we explain the constant $e$. I have searched a lot for it. But I couldn't ...
4
votes
1answer
157 views

Euler's Question

I came across this problem that I would like to ask you about: For which values $a>0$ does there $\exists$ a limit of the sequence $$a, a^{a},a^{a^{a}}, a^{a^{a^{a}}}...$$ Well this looks like a ...