Question 800321
Let {{{ P }}} = the starting population
Let {{{ p }}} = the population for the current year
Start of 1st year:
{{{ p = P }}}
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Start of 2nd year:
{{{ p = P + .1P }}}
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Start of 2nd year:
{{{ p = P + .1P + .1*( P + .1P ) }}}
{{{ p = ( P + .1P )*( 1 + .1 ) }}}
{{{ p = P*( 1 + .1 )^2 }}}
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Start of 3rd year:
{{{ p = P*( 1 + .1 )^3 }}}
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In what year {{{ n }}} will {{{ p = 2P }}}?
{{{ 2P = P*1.1^n }}}
{{{ 2 = 1.1^n }}}
{{{ n*log(1.1) = log(2) }}}
{{{ n = log(2) / log(1.1) }}}
{{{ n = .301 / .0414 }}}
{{{ n = 7.271 }}}
After 7 years the population is doubled
check:
{{{ 2 = 1.1^n }}}
{{{ 2 = 1.1^7.271 }}}
{{{ 2 = 1.9997 }}}
close enough