Question 1129160
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In 12 minutes, the number of students who know the rumor increases from 2 to 15, a growth factor of 15/2 = 7.5.  The number will continue growing by a factor of 7.5 every 12 minutes; we want to know how many minutes it will take for all 1250 students to know the rumor.<br>
If n is the number of 12-minute intervals, then the number of students who know the rumor is given by the exponential function<br>
{{{2(7.5)^n}}}<br>
So we need to solve<br>
{{{2(7.5)^n = 1250}}} or {{{(7.5)^n = 625}}}<br>
With the n as an exponent, we need to use logarithms:<br>
{{{log(((7.5)^n)) = log((625))}}}
{{{n*log((7.5)) = log((625))}}}
{{{n = log((625))/log((7.5))}}} = 3.195 to 3 decimal places.<br>
So the time required for all 1250 students to know the rumor is 12*3.195 = 38.34; or 38 minutes to the nearest minute.