anonymous
  • anonymous
The size of an exponentially growing bacteria colony doubles in 2 hours. How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form. Exact form
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Exponential growth and the double growth indicates the population size is modeled by \[y=a(2^{rx})\] with \(a\) being the initial population, \(r\) being the relative growth factor, and \(x\) is time. The population doubles in 2 hours, so when \(x=2\), you have \[2a=a2^{2r}\\ 2=2^{2r}\\ 1=2^{2r-1}\\ r=\frac{1}{2}\] So you have to find \(x\) such that \(y=3a\): \[3a=a\left(2^{x/2}\right)\] Sounds right, at any rate. I might be wrong.
wolf1728
  • wolf1728
If it doubles every 2 hours then formula is 2^((t-2)/2) you want to solve when 2^((t-2)/2) = 3
anonymous
  • anonymous
@wolf1728 So i solve 2^((t-2)/2)=3 ?

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anonymous
  • anonymous
for t?
anonymous
  • anonymous
|dw:1378598586183:dw| Is this right?
anonymous
  • anonymous
that gives you a t of 21.something ---that can't be right but I was hopin to find out the right answer too
anonymous
  • anonymous
I have no idea
wolf1728
  • wolf1728
2^((t-2)/2) = 3 n_Douglas yes solve for t by taking logs of both sides ((t-2)/2)* log(2) = log3 ((t-2)/2)*.3010299957= 0.4771212547 ((t-2)/2)= 0.4771212547 / .3010299957 ((t-2)/2) = 1.5849625007 multiplying by 2 (t-2) = 3.1699250014 t = 5.1699250014 After 4 hours the population has doubled. After 5.1699250014 hours population has tripled.
anonymous
  • anonymous
easier with sith's equation I think 2=2^(t/2) so to triple that means 3=2^(t/2) ln both sides ln3=ln2* (t/3) divide by ln2 ln3/ln2 = t/3 multiply by 3 and t= 3 ln3/ln2 which the calculator says is 4.75 which seems closer
anonymous
  • anonymous
wolf the problem says the population doubles in 2
wolf1728
  • wolf1728
The population doubles every 2 hours. So let's suppose after 2 hours population = 250 After 4 hours it is 500
anonymous
  • anonymous
right to P0 would have been 125 we are looking for P(t) of 375
wolf1728
  • wolf1728
Well then if that's the case then it is 3.17 hours. Yes, I kept hanging around here because I was wondering how to interpret the question. So, 3.17 is the answer. (or 5.17 if you take the population after 2 hours as the beginning.
anonymous
  • anonymous
3 hours intuitively seems like the right time
anonymous
  • anonymous
((t-2)/2)* log(2) = log3 if i were to look for an exact formula then would i still find for t?
wolf1728
  • wolf1728
Yes, you would still solve for t
wolf1728
  • wolf1728
Of course that is an exact formula :-)
anonymous
  • anonymous
So it will come up at t=2log(3/2)+2
wolf1728
  • wolf1728
I'm glad I stuck around (as well as you folks) because I was wondering if my formula was right and if I could solve for 't'. Nice to see there's some inquisitive folks here at Open Study.
wolf1728
  • wolf1728
ndouglas - I have it all worked out about half way up the page.
wolf1728
  • wolf1728
Remember in my calculations, I took the starting point as 2 hours. Also, I use common logs (just used to those.)
anonymous
  • anonymous
I see it now. thanks
wolf1728
  • wolf1728
All right. Yeah I just wanted to make sure we ALL understood this problem.
anonymous
  • anonymous
thanks wolf I'll try it now on paper
wolf1728
  • wolf1728
okay kantalope - think I'll leave this topic now. c ya folks later :-)

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