SOLUTION: The number of bacteria N in a culture is modeled by N = 100 ekt where t is the time in hours. If N=150 when t=3, what is the time (in hours) required for the original pop

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The number of bacteria N in a culture is modeled by N = 100 ekt where t is the time in hours. If N=150 when t=3, what is the time (in hours) required for the original pop      Log On


   

Question 866914: The number of bacteria N in a culture is modeled by
N = 100 ekt
where t is the time in hours. If N=150 when t=3, what is the time (in hours) required for the original population to double in size ?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
NOT this, N = 100 ekt,
but THIS: N=100e%5E%28kt%29.

You want to first find what is k.
ln%28N%29=ln%28100%29%2Bkt%2A1
kt=ln%28N%29-ln%28100%29
highlight_green%28k=%281%2Ft%29ln%28N%2F100%29%29
Substituting the given data from the description,
k=%281%2F3%29ln%28150%2F100%29
k=%281%2F3%29ln%281.5%29
highlight_green%28k=0.135%29

Now you have the model as highlight%28N=100e%5E%280.135t%29%29.

Remember this:kt=ln%28N%29-ln%28100%29
Now, since you want to know t for when N=200, solve for t, ...
t=%281%2F0.135%29%28ln%28200%2F100%29%29