Wednesday

July 23, 2014

July 23, 2014

Posted by **Jen** on Friday, February 16, 2007 at 10:22pm.

Find a function that models the number of bacteria n(t) after t hours.

The answer is n(t) = 8600e^.1506t

Where does this 0.1506 come from?

Thanks.

n(t) = 8600 e^(kt), where k is an unknown constant and t is the number of hours. We know that n(1), or the population after one hour is 10000. So 10000 = 8600e^(k*1)

10000/8600 = e^k

natural log ln(10000/8600) = k = .1508

The general expression is n(t) = no* e^(t/T), where T is the time for an increase by a factor of e.

In this case,

10000 = 8600 e^(1/T)

That equation can be solved for T.

10000/8600 = 1.16279 = e^(1/T)

Take the natural log of both sides.

0.15082 = 1/T

n(t) = e^(0.15082 t)

The 0.1506 in your version is not quite right.

**Related Questions**

Precalculus - NEED HELP ASAP PLEASE!! A bacteria culture starts with 2000 ...

Calc - The number of bacteria in a culture is increasing according to the law of...

precalculus - A bacteria culture initially contains 1500 bacteria and doubles ...

MATH :) - 3. In Biology, it is found that the bacteria in a certain culture ...

Math - A culture contains 12,000 bacteria. After an hour the count is 25,000. ...

Algebra 2 - If there are initially 1500 bacteria in a culture, and the number of...

math - The number of bacteria in a culture is modeled by: n(t) = 1330e^(0.42t) (...

Calculus - Suppose that a population of bacteria triples every hour and starts ...

Math - he number of bacteria in a culture is modeled by n(t)=1710e071t (a) The ...

math - The number of bacteria in a culture is modeled by n(t)=1710e071t (a) The ...