Question 1147675
{{{ P = P(0)*( 1 + r )^t }}}
{{{ 200 = P(0)*( 1 + r )^15 }}}
{{{ 200/P(0) = ( 1 + r )^15 }}}
and
{{{ 2000 = P(0)*( 1 + r )^40 }}}
{{{ 2000/P(0) = ( 1 + r )^40 }}}
{{{ 200/P(0) = (1/10)*( 1 + r )^40 }}}
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{{{ ( 1 + r )^15 = (1/10)*( 1 + r )^40 }}}
divide both sides by {{{ ( 1 + r )^15 }}}
{{{ 1 = (1/10)*( 1 + r )^25 }}}
{{{ 10 = ( 1 + r )^25 }}}
Take the log base 10 of both sides
{{{ 1 = 25*log( 1 + r ) }}}
{{{ log( 1 + r ) = .04 }}}
{{{ 1 + r = 10^.04 }}} ( I'll refer back to this step )
{{{ 1 + r = 1.09648 }}}
{{{ r = .09648 }}}
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To find doubling period:
{{{ 2P(0) = P(0)*( 1 + r )^t }}}
{{{ 2 = ( 1 + r )^t }}}
Take log base 10 of both sides
{{{ log(2) = t*log( 10^.04 ) }}} ( from the above mentioned step )
{{{ .30103 = t*.04 }}}
{{{ t = 7.526 }}} 
The doubling period is 7.526 min
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