SOLUTION: The number of bacteria present in a culture after t minutes is given as B=10e^kt. If there are 6703 bacteria present after 5 minutes, kind k.

Question 307675: The number of bacteria present in a culture after t minutes is given as B=10e^kt. If there are 6703 bacteria present after 5 minutes, kind k.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

, solve for k.

Divide both sides by 10:

Take the ln of each side:

Divide both sides by 5:

Using a calculator:
k=1.301545075, round off to k=1.30.

I have quite a bit of explanation with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the links on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time" and also "MATH IN LIVING COLOR", and look under "College Algebra" (Chapter 4), Section 4.05 Applications--Growth and Decay. The explanations on the MATH IN LIVING COLOR pages are complete with use of the GRAPHING CALCULATOR (TI84).

I also have an entire explanation of Logarithms on video from my own teaching in class before I retired a few years ago. To see the videos, look for "Rapalje Videos in Living Color", and see College Algebra for the topic of Logarithms.

I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. My own students did!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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