Question 1028864
Let {{{ A }}} = the population at the start
Let {{{ t }}} = years it takes population to double
{{{ 2A }}} = the population after {{{ t }}} years
{{{ r = .13 }}} = yearly rate of increase
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The formula is:
{{{ 2A = A*( 1 + .13 )^t }}}
Divide both sides by {{{ A }}}
{{{ 2 = 1.13^t }}}
Take the log of both sides
{{{ log(2) = t*log( 1.13 ) }}}
{{{ t = log(2) / log( 1.13 ) }}}
{{{ t = .30103/.05308 }}}
{{{ t = 5.671 }}}
In 5.7 yrs the population will be
double what it started as.
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check:
{{{ 2 = 1.13^t }}}
{{{ 2 = 1.13^5.671 }}}
{{{ 2 = 1.999898 }}}
close enough