SOLUTION: The population of a colony of bacteria increases exponentially with time. If the population starts with 8000 bacteria and 4 hours later the population is 10000... a.) when will

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Question 1002149: The population of a colony of bacteria increases exponentially with time. If the population starts with 8000 bacteria and 4 hours later the population is 10000...
a.) when will the population be 12000?
b.) what is the doubling time?
c.) what will the population be after 10 hours?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
In general, exponential growth takes the form
A%28t%29+=+Ao%28e%5E%28kt%29%29
Let's plug in to find k...
10000=8000%2Ae%5E%284k%29
1.25+=+e%5E%284k%29
ln%281.25%29+=+4k
k = ln(1.25)/4 = .05579
Now plug that into
A%28t%29+=+Ao%28e%5E%28kt%29%29 to get
A%28t%29+=+Ao%28e%5E%28.05579%2At%29%29
and for your case
A%28t%29+=+8000%2A%28e%5E%28.05579%2At%29%29
Now plug in 12000 for A(t) to find t for part a,
plug in 16000 for A(t) to find t for part b,
and plug in 10 for t to find A(t)for part c.