a colony of bacteria starts with 900 cells and triples in size every 8 hours. find a function of population growth of this colony of bacteria with time, t, in hours.

and how many cells will be in the colony after 20 hours?

Question

a colony of bacteria starts with 900 cells and triples in size every 8 hours.  find a function of population growth of this colony of bacteria with time, t, in hours.  

and how many cells will be in the colony after 20 hours?

mertsj · Answer

14,030

mertsj · Answer

$$P(t)=900e ^{.137326t}$$

anonymous · Answer

the equation did not look right to me... doesn't work either.

mertsj · Answer

Did the 14,030 work?

anonymous · Answer

yep haha

mertsj · Answer

Then the equation is correct because that is what I used to get the 14,030

mertsj · Answer

Probably used too many digits for the constant.

anonymous · Answer

nope, i doubt i should have e in there

mertsj · Answer

You'd better check your exponential growth equation then.

anonymous · Answer

the hint I'm given to help is "p(t)=initial population at 0*2^t/time units

mertsj · Answer

$$A=a _{0}e ^{kt}$$

mertsj · Answer

What does 0*2^t mean?

anonymous · Answer

0 is mean to go with the population.  "population at time 0"*2^t(hours)/d(time units)

anonymous · Answer

just got it

anonymous · Answer

was p(t)=900*3^t/8

mertsj · Answer

Ok.  Try this:  
$$P(t)=900(2)^{.198120t}$$

anonymous · Answer

i had a feeling i didn't need the heavy exponent

mertsj · Answer

where did you get t/8?

anonymous · Answer

i more or less just tried things.  t stood for hours and the colony tripled its size every 8 hours

mertsj · Answer

ok