Question 290509
The bacteria E Coli are found in the human bladder. Suppose 1,000 bacteria are present at time t = 0. Then, t minutes later the number of bacteria present can be approximated by N(t) = 1000(3)t/12.
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I think your equation is really:
{{{N(t) = 1000(3)^(t/12)}}}
This is an "exponential growth" equation.
Where
N(t) is the bacteria count
t is time (in minutes)
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How many bacteria will be present after 40 minutes?
Simply substitute 40 for t and solve:
{{{N(t) = 1000(3)^(t/12)}}}
{{{N(40) = 1000(3)^(40/12)}}}
{{{N(40) = 1000(3)^3.333}}}
{{{N(40) = 38940.74}}}
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How long will it take before there are 100,000 bacteria present?
The 100,000 is N(t) so you would need to solve for t:
{{{N(t) = 1000(3)^(t/12)}}}
{{{100000 = 1000(3)^(t/12)}}}
{{{100 = (3)^(t/12)}}}
{{{log(3,100) = t/12}}}
{{{12log(3,100) = t}}}
{{{50.30 = t}}}  (minutes)
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