f(0)=10, f(12)=8, f(24)=7 f(36)=6,5, f(48)=6. I know how to construct an exponential function if I have two points, but I don't know how to create this function, or that such exponential functian even exists.

django0a6
2022-11-20
Answered

You can still ask an expert for help

Berattirna

Answered 2022-11-21
Author has **19** answers

If A is not invertible, then consider a matrix V associated to some non-zero linear map that is 0 on $\mathrm{col}A$. Then, $VA=0$ and $V\ne 0$

asked 2022-11-11

Exponential functions has the format :

$\begin{array}{r}numbe{r}^{x}\end{array}$

But these functions are not exactly power x, so I am confused:

$\begin{array}{r}{\sqrt{5}}^{{\mathrm{log}}_{5}x}\\ {8}^{\mathrm{lg}x}\end{array}$

Help me to understand the classes of function, so I would like to know what class are the above 2 functions in

$\begin{array}{r}numbe{r}^{x}\end{array}$

But these functions are not exactly power x, so I am confused:

$\begin{array}{r}{\sqrt{5}}^{{\mathrm{log}}_{5}x}\\ {8}^{\mathrm{lg}x}\end{array}$

Help me to understand the classes of function, so I would like to know what class are the above 2 functions in

asked 2022-11-15

$f:\mathbb{R}\to \mathbb{R},\phantom{\rule{1em}{0ex}}x\mapsto a{b}^{x}$

for the case a>0 and b>1.

I`m interested in other examples which are in some way fascinating or funny for this case.

I don't want any discrete examples or such involving the Euler number e. Any suggestions for that?

for the case a>0 and b>1.

I`m interested in other examples which are in some way fascinating or funny for this case.

I don't want any discrete examples or such involving the Euler number e. Any suggestions for that?

asked 2022-06-24

asked 2022-11-24

the equation f(x)′−f(x)=0 holds for the exponential function on the complex plane.Now what i dont understand is this.

"let $f(x)={a}_{0}+{a}_{1}X+{a}_{2}{X}^{2}........$ f is a polynomial with infinite degree ".Why is that. I dont understand how he came to that conclusion?I mean Why define it that way?.MAybe he could solve the ODE on the real numbers and avoid this "out of nowhere" polynomial or is there a connection?

"let $f(x)={a}_{0}+{a}_{1}X+{a}_{2}{X}^{2}........$ f is a polynomial with infinite degree ".Why is that. I dont understand how he came to that conclusion?I mean Why define it that way?.MAybe he could solve the ODE on the real numbers and avoid this "out of nowhere" polynomial or is there a connection?

asked 2022-11-08

IProve that exponential functions ${a}^{n}$ have different orders of growth for different values of base a>0.

It looks obvious that when a=3 it grows faster when compared to a=2. But how do i make a formal proof for this? Thanks for your help.

It looks obvious that when a=3 it grows faster when compared to a=2. But how do i make a formal proof for this? Thanks for your help.

asked 2022-07-15

How do I find vertical asymptotes using an exponential function? ($f(x)=a{b}^{x-h}+k$)I know that horizontal asymptotes are y = k, but I don't know how to find the vertical ones

asked 2022-10-12

Why the derivatives of exponential functions, lets say, as apposed to polynomials, grow more rapidly than the functions themselves?

i.e.

$$y={e}^{{x}^{2}}\phantom{\rule{0ex}{0ex}}\frac{\mathrm{d}y}{\mathrm{d}x}=2x{e}^{{x}^{2}}$$

I am interested in a verbal explanation.

i.e.

$$y={e}^{{x}^{2}}\phantom{\rule{0ex}{0ex}}\frac{\mathrm{d}y}{\mathrm{d}x}=2x{e}^{{x}^{2}}$$

I am interested in a verbal explanation.