Question 768201
For now,
Let {{{ a }}} = initial population
Let {{{ P }}} = current population
Let {{{ k }}} = years to double population
Let {{{ n }}} = number of {{{ k }}} doubling periods 
it takes to reach target
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Initially,
{{{ n = 0 }}}
{{{ P = a*2^n }}}
{{{ P = a }}}
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After {{{ k }}} years
{{{ n = 1 }}}
{{{ P = a*2^1 }}}
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After {{{ 2k }}} years
{{{ n = 2 }}}
{{{ P = a*2^2 }}}
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So, in general, after {{{ n*k }}} years,
{{{ P = a*2^n }}}
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Now fill in values:
{{{ k = 41 }}} years
{{{ a = 310 }}} million
{{{ P = 350 }}} million
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{{{ 350 = 310*2^n }}}
{{{ 2^n = 350/310 }}}
{{{ 2^n = 1.12903 }}}
Take the log of both sides
{{{ n*log( 2 ) = log( 1.12903 )
{{{ n = log( 1.12903 ) / log( 2 ) }}}
{{{ n = .05271 / .30103 }}}
{{{ n = .1751 }}}
{{{ n*k = .1751*41 }}}
{{{ n*k = 7.179 }}}
In 7.2 years, the population of 350 million will be reached
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check answer:
{{{ 350 = 310*2^n }}}
{{{ 350 = 310*2^.1751 }}}
{{{ 2^.1751 = 35/31 }}}
{{{ 1.12904 = 1.12903 }}}
close enough