Question 212974
Starting with 25,000 bacteria present at time zero, you can write:
{{{N(t) = 25000(2)^(t/20)}}} Note: The exponent is really = {{{t/20}}}
At what time,t, will the bacteria count reach 100,000,000? Set N(t) = 100,000,000 and solve for t.
{{{100000000 = 25000(2)^(t/20)}}} Divide both sides by 25000.
{{{4000 = (2)^(t/20)}}} Take the logarithm of both sides.
{{{log((4000)) = log((2))^(t/20)}}} Apply the power rule for logarithms.
{{{log((4000)) = (t/20)log((2))}}} Divide both sides by {{{log((2))}}}
{{{t/20 = log((4000))/log((2))}}} Multiply both sides by 20.
{{{t = 20*log((4000))/log((2))}}} Evaluate.
{{{t = 239.3156}}}Minutes. Round up to:
{{{t = 240}}}Minutes.  Convert to hours. {{{240/60 = 4}}}
{{{t = 4}}}hours. Add this to 11:00am to get 15:00 hours. Subtract 12 hours.
Time = 3:00pm
Infection can occur at 3:00pm