Math Is Fun Forum

be the book said :-

{ show that the population grew by a factor of about 1.034, or 3.4%, every year. Whenever we have a constant growth factor (here 1.034), }

isn't constant growth factor should be only 0.034? without 1

the book saying  ( 1.034 or! 3.4% )
isn't he should say ( 0.034 or 3.4%)

and the is the number called exponential factor

so what is the correct to say now pls tell
is the exponential growth say to it ( 0.034 or 3.4% ) or ( 1.034 or 3.4%)

but what is the meaning of that  0.0000001

what is this? I see that number or similar in most books specially books about probability
it called tolerance number or  accuracy number or something like that

this condition  <   0.0000001 is driving me crazy
why smaller than? and why this number with these zeros

thanks now everything almost clear thank you very much

you rounded 0.347/12.853 = 0.03399984439 to 0.034
I read the round subject on the site

but I still wonder is that legal to do in every number?
isn't that will make mistakes and arithmetic glitch 
I mean when round these numbers ain't they will effect the result and cause a system fail
because this is not accurate, when I would round number and where ? and when and where not?

and is that right?

please admin answer me two question separately because I'm very beginner don't merge the ideas for me it will hard for me to read and unerstand

you said :

new amount in the account = old amount plus interest less the monthly amount out

you mean : p_new = 10000 + 10050 - 500 = 19550 ?

but I thought the  amount will be only : 10000 + 0.5% = 10050 in the first month

you are saying old amount plus interest
why did you put two p_old!

sorry but I didn't understand the first movements

it's like you rote p_new = p_old + M - M !
because M = ( p * r/100 )
why this step?

can you give me values step by step for the first 3 months please

before that pls see how is my calculations :-

balance = 10,000 + 0.5% = 10050
now 10050 - $500 = 9950
now add 9950 + 0.5% = 9597.75
after that again sub 9597.75 - $500
to the end....
and in my calculations the algorithm will stop because the account balance will be less than $500 so can't withdraw from it again

what is wrong in my calculations?

oh I didn't notice that how could I didn't focus I was focus in read this but u helped me finally

I have another question
the account won't be depleted because when we add 500 to 10,000
than sub 500
nothing will change the account won't be $0

what is the value in the question that I can change to make the account depleted ?

and the full exercise is :

Write an algorithm to settle the following question: A bank account starts out with $10,000. Interest is compounded monthly at 6 percent per year (0.5 percent per month). Every month, $500 is withdrawn to meet college expenses. After how many years is the account depleted?

the problem is I don't want only the answer I want to analyse the answer and the steps to have fully understand about that problem

in math is fun I saw this example about convert a percent to a fraction pls look at the following picture :-

the question here is what if it was 2 digits after the decimal point ?
like the previous number 222.10%
when I was trying to convert it to fraction
I stuck into the second step
222.10/100 * 10/10 ? or 100?100 or multiply by 1000/1000?

the example of math if sun was 62.5% and they mentioned that they multiply both top and bottom by 10!! because there is 1 digit after the decimal point

in my number 222.10% there is 2 digits! 1 and 0
so do I have to multiply top and bottom by 100?
or 1000? or 10?