SOLUTION: Population of a particular bacterial colony; i.e. the number of cells at time t (hours) is given by the function (N(t)=N0^e^kt) where k is the growth constant When this bacterium

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Question 1161540: Population of a particular bacterial colony; i.e. the number of cells at time t (hours) is given by the function (N(t)=N0^e^kt) where k is the growth constant
When this bacterium is grown under ideal laboratory conditions, the number of
cells in a culture doubles every 30 minutes. Find the value of k to 2 decimal
places
How Do I find K value for this question?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

You start from N = N(0) bacteria.


After 30 minutes, you have 2N(o) bacteria, which gives you THIS EQUATION


    2N(0) = .


Next, you divide both sides by N(0). You get then 

   
    2 = .


Now, you take natural logarithm of both sides


    ln(2) = 30k.


Hence,  k =  = USE YOUR CALCULATOR = 0.023105


and you can round this value AS YOU WANT.

Solved.

Is my explanation clear to you ?

If you still have questions, do not hesitate to ask me.

---------------

On this subject,  see my lesson
    - Bacteria growth problems
in this site.

From this lesson you may learn everything, what a student should know about it . . .

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



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