Question 251387
{{{N(t) = 2000*3^(t/12)}}}
given:
{{{t = 40}}} min
{{{N(40) = 2000*3^(40/12)}}}
{{{N(40) = 2000*3^(10/3)}}}
{{{N(40) = 2000*38.94}}}
{{{N(40) = 77881}}}
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given:
{{{N(t) = 100000}}}
{{{100000 =2000*3^(t/12)}}}
{{{50 = 3^(t/12)}}}
Take the log of both sides
{{{log(50) = log(3^(t/12))}}}
{{{1.69897 = (t/12)*log(3)}}}
{{{1.69897 = .47712*(t/12)}}}
{{{t/12 = 1.69897/.47712}}}
{{{t/12 = 3.56088}}}
{{{t = 42.73}}} min