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January 30, 2015

January 30, 2015

Posted by **Rani** on Wednesday, October 7, 2009 at 3:06pm.

One equation that may be useful is:

Pt = Po * (1 + {GR/100})n

Science!! Please HELP - MathMate, Wednesday, October 7, 2009 at 12:08am

Apply the given formula,

P(t) = Po(1+r)n

where

r=0.03 is the annual growth rate in percent divided by a hundred.

n=number of years

Po=initial population=10000

For 1 year,

P(1) = 10000*(1.03)1

=10300

P(15)=10000*(1.03)15

= ______

P(100)=10000*(1.03)100

=_______

The doubling time is rougely 24 years using the rule of 72 (72 divided by the annual rate of interest).

The exact doubling time is log(2)/log(1.03)

=23.45 years.

Time required to grow from 10000 to 1920000 is

log(1920000/10000)/log(1.03)

=______ years

OK I understand the 1og2/log1.03 but when i calculate it i get

0.01280....

and why do you need to divide by 72? what is the prupose and where do you divide it i dont understand that part.

- Science!! Please HELP -
**DrBob222**, Wednesday, October 7, 2009 at 3:20pmlog 2/log 1.03 = 23.44977. The mistake you are making is log 1.03 is 0.0128. You must divide that number into log 2 which is 0.30103 and you will obtain 23.45 if you do that (23.44977 to be exact about it).

There is no divide by 72 in Mathmate'e response although there is a divide**into 72**. The rule of 72 is a quick short cut rule which is 72/annual rate of interest and this gives the approximate time for doubling. 72/3 = 24 years which is close to the actual time of 23.45 which Mathmate calculated for you.

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