Math Is Fun Forum

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Family of Exponential Functions

Hi, please see this picture
and if may you tell me what is the meaning of  a = c < p ?
and what is the benefit from this, why the solution of the book for this example give these details
is there other solution? I mean maybe I can comments on these values different from what the solution of the book said

I mean just tell me one thing please what the book solution wanted me to know about this?

Last edited by Hannibal lecter (2019-09-24 02:26:05)

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Family of Exponential Functions

When I get stuck trying to learn a new topic in maths, I try out lots of examples to see what happens.  So I suggest you experiment with lots of exponential graphs.

Go to this page: https://www.mathsisfun.com/data/function-grapher.php  and try the following:

1) exp(x)  This will show you the basic exponential graph  (exp here is the constant e, so you are plotting e^x)
 
Then try

2) 2exp(x) and 3exp(x) etc to see the effect of a multiplier .

3) Then exp(-x)

You can try put a variety of numbers.

Then try

4) 2^x

5) 3^x

6) 2^(-x)

A graph of the form a^(x) can always be changed into an exp graph as follows:

let y = a^x

Take logs

ln(y) = x.ln(a)

raise each side to the power 'e'

e^ln(y) = y = e^[x.ln(a)]

Hopefully this will help you with all the questions you have posted yesterday.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: Family of Exponential Functions

thank you very very much,,

actually I post a new posts today it's very necessary to me names :-

http://www.mathisfunforum.com/viewtopic.php?id=25240
http://www.mathisfunforum.com/viewtopic.php?id=25239

because there is some conflicts in my mind about a few things

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Family of Exponential Functions

I didn't notice you had logged on while I was making my post.  I edited the wording so please check you have read the up-to-date post.

I think you can also use the graph plotter to help with those other questions.

eg.  Try 7)  S(1 − e^(−kt) ) with values of S and k that you choose.

and 8) 5(1 .07)^x

Bob

ps.  Once you have tried all of these, try all your questions again and post here if you are still needing help.  To keep it simple I will not post in those threads as well.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: Family of Exponential Functions

I'm using
https://www.desmos.com/calculator
is that okay with it

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Family of Exponential Functions

I've not used it until today.  It looks like it will do the same job. 

You have to input the whole equation eg. y = e^x  (On the MathsisFun grapher, the y = is done for you.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: Family of Exponential Functions

I did it and the and read the example again not it's clear thank you
and I understand now how the ln is an inverse of e

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Wisdom is a tree which grows in the heart and fruits on the tongue