SOLUTION: You are studying a new breed of bacteria whose population grows exponentially following the model y= 80e^kt where t is the time in seconds. a) If the initial population is 80 ce

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Question 867803: You are studying a new breed of bacteria whose population grows exponentially following the model y= 80e^kt where t is the time in seconds.
a) If the initial population is 80 cells and after 30 minutes there are 675 cells, determine the growth coefficient k.
b) How long will it take for the bacteria population to reach 6000 cells ?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
y= 80e^kt
Show the equation as y=+80e%5E%28kt%29.
Description suggests t will be in minutes.

Part (a):
ln%28y%29=ln%2880%29%2Bkt
kt=ln%28y%29-ln%2880%29
k=%281%2Ft%29%28ln%28y%2F80%29%29
-
k=%281%2F30%29%28ln%28675%2F80%29%29
k=2.132686%2F30
highlight_green%28k=0.07109%29
Model is specifically y=80e%5E%280.07109t%29.