SOLUTION: A biologist is researching a newly discovered species of bacteria. At time T equals zero hours, he put 100 bacteria into what he has determined to be a favorable growth medium. Six

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A biologist is researching a newly discovered species of bacteria. At time T equals zero hours, he put 100 bacteria into what he has determined to be a favorable growth medium. Six      Log On


   

Question 1209240: A biologist is researching a newly discovered species of bacteria. At time T equals zero hours, he put 100 bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant K for the bacteria? (Round K2 decimal places) By what hour to the nearest 10 will there be 1000 bacteria?
Answer by timofer(105) About Me  (Show Source):
You can put this solution on YOUR website!
You could choose this form for the growth model:
p=a%2Ae%5E%28Kx%29


Your given starting information means, by substitution,
450=100e%5E%286K%29

Take natural log of both sides.
ln%28450%29=ln%28100%29%2B6K%2Aln%28e%29
ln%28450%29-ln%28100%29=6K
K=%28ln%28450%29-ln%28100%29%29%2F6
and you can compute this...