The number of bacteria present in a culture after  T  minutes is given
as B=100e^kt (to the kt). If there are 52, bacteria present after 13
minutes, find  k.

Hello Bedhog,

Let us walk through the formula and explain how to get to the correct answer.

[0] What you know...
  B = 100 * e^(k*t)
  B = 52 when t = 13

You must get the unknown value (k) on one side of the equation without
any other factors to "solve" the equation.

[1] Divide both sides by 100.
  B/100 = e^(k*t)

[2] Take the logarithm of both sides to eliminate the exponent.
  ln (B/100) = k*t

[3] Divide both sides by t
  ln (B/100)/t = k
or
  k = ln (B/100)/t

Now we have the unknown value (k) on one side and the other side has
only known values.

[4] Plug in the known values
  k = ln (52/100)/13
  52/100 = 0.52
  ln (0.52) = -0.653926467
  k = -0.653926467/13 = -0.050302036
or
  k = -0.050302036

[5] Cross check with original formula
  B = 100 * e^(k*t)

Does 52 = 100 * e^(-0.050302036*13)?

The result of the right hand side on the calculator I used was 52, so
this value of k satisifes the formula provided (to the precision of my
calculator). You may get slightly different answers with your
calculator - I suggest you repeat the steps to ensure you get an
answer similar to this one (it may have more / less precision).

Other examples like this one (and other methods to solve them) can be
found with search phrases such as
  solve equation exp
or a site like
  http://library.thinkquest.org/20991/alg2/log.html

If this answer is unclear or you need a more complete explanation,
please make a clarification request.

  --Maniac

thanks for your help. would you two more?

B=100e^kt 
B=52
t=13

52=100e^13k
52/100=e^13k
.52=e^13k
ln .52= ln e^13k
ln .52=13k
(ln .52)/13=k
ln .52 = 1.68
1.68/13=k
k = .1292

Am I right? It's been a long time since I did that kind of math and
wanted to see if I could get it.

who said ln .52 = 1.68....are u joking?

ln .52=-.06539

As I recall, the ln of any number 0< n <1 will always be a negative number.

I'm not sure if this is correct, but it seems logical...

B=100e^kt
where B=52 and t=13

1) 52=100e^13k
2) 52/100=e^13k
3) ln(52/100)=13k
4) k=ln(52/100)/13
5) k=-0.05

Remember this is with time in minutes. If time is to be measured in
seconds, step 4 would have to be divided by 780 instead of 13.

Here's the easiest way to get the answer to the original question

://www.google.com/search?hl=en&lr=&safe=off&q=ln%2852%2F100%29%2F13&btnG=Search