Question 640953
Let the initial population = {{{ p }}}
After 5 days {{{ 3p }}}
After 10 days {{{ 9p }}}
After 15 days {{{ 27p }}}
After 20 days {{{ 81p }}}
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If n = 1,2,3,4,5, ( any whole positive number )
After {{{ 5n }}} days, population = {{{ p*3^n }}}
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By factor, they mean what is the multiplier?
If {{{ p = 1000 }}} and
{{{ 5n = 10 }}}
{{{ n = 2 }}}
{{{ p*3^n = 1000*3^2 }}}
{{{ p*3^n = 9000 }}}
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What factor do you multiply 1000 by to get 9000 ?
The factor is {{{ 9 }}}
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At what time t, in days will the population have increased by a factor of 6? 
{{{ 6*1000 = 6000 }}}
They want days, which is {{{ t = 5n }}}
{{{ 1000*3^n = 6000 }}}
{{{ 3^n = 6 }}}
Take the log base 10 of both sides
{{{ log( 3^n ) = log( 6 ) }}}
{{{ n*log(3) = log(6) }}}
{{{ n = log(6) / log(3) }}}
{{{ t = 5n }}}
{{{ t = 5*( log(6) / log(3)) }}}
Calculate the logs, do the division, and 
round off to the nearest day