Question 1029066
The total number of people after each hour is:
(0) {{{ 2^1 }}}
(1) {{{ 2^1 + 2^2 }}}
(2) {{{ 2^1 + 2^2 + 2^3 }}}
(3)  {{{ 2^1 + 2^2 + 2^3 + 2^4 }}}
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I notice that at hour number {{{ n }}},
the total that hear rumor is {{{ 2^( n + 2 ) - 2 }}}
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I can say:
{{{ 450 = 2^( n + 2 ) - 2 }}}
{{{ 452 = 2^( n + 2 ) }}}
{{{ 452 = 2^n*2^2 }}}
{{{ 452 = 4*2^n }}}
{{{ 2^n = 113 }}}
{{{ n*log(2) = log(113) }}}
{{{ .30103n = 2.05308 }}}
{{{ n = 6.8202 }}}
{{{ .8202*60 = 49.21 }}}
All 450 students hear rumor after
6 hrs and 49 min
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check:
{{{ 450 = 2^( n + 2 ) - 2 }}}
{{{ 450 = 2^( 6.8202 + 2 ) - 2 }}}
{{{ 450 = 2^8.8202 - 2 }}}
{{{ 450 = 452.007 - 2 }}}
{{{ 450 = 450.007 }}}
error due to rounding off
You might want a 2nd opinion on this