Problema Solution

A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts two hundred bacteria into what he has determined to be a favorable growth medium. Eight hours later, he measures 1200 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to three decimal places.)

Answer provided by our tutors

The exponential growth of the bacteria is described with the formula:


A = Pe^(kt)


For t = 0 hours P = 200 bacteria


The ending amount is A = 1,200 bacteria at t = 6 hours.


Plug in all the known values into A = Pe^(kt) , and then solve for the growth constant k:


1200 = 200*e^(6k)


200*e^(6k) = 1200

........

........ k = 0.299 The growth constant is 0.299 (rounded to third decimal). The growth constant is 0.25/hour.