Question 788593
Amount saved each month:
1st month: 20
2nd month: 2*20
3rd month: 4*20
4th month: 8*20
etc.
Summing up the amounts saved:
{{{ 20 + 2*20  4*20 + 8*20 }}} etc,.
{{{ 20*( 1 + 2 + 4 + 8 ) }}} etc.
{{{ 20*( 2^n - 1 ) }}}
where {{{ n }}} is the number of months
given:
{{{ 20*( 2^n - 1 ) = 1200 }}}
{{{ 2^n - 1 = 60 }}}
{{{ 2^n = 61 }}}
Take log base 10 of both sides
{{{ n*log(2)  = log(61) }}}
{{{ .301n = 1.785 }}}
{{{ n = 5.931 }}}
She will have enough money in about 6 months
check:
{{{ 20*( 1 + 2 + 4 + 8 + 16 + 32 ) = 20*63 }}}
{{{ 20*63 = 1260 }}}
At the end of only 5 months, she has:
{{{ 20*( 1 + 2 + 4 + 8 + 16 ) = 20*31 }}}
{{{ 20*31 = 620 }}}
OK