Help with Geometric sequence

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Jyashi
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I am ok with the Part A side of the questions and i know the sequence is 2 (2)^t or (2)^t+1

What i am strugling with is the Part B side as i dont know how to extend this model using Algebra. Do you guys know how to tackle the part B of the question and any ideas on what models i can use?Name:  sequence screenshot.jpg
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Gregorius
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(Original post by Jyashi)
I am ok with the Part A side of the questions and i know the sequence is 2 (2)^t or (2)^t+1

What i am strugling with is the Part B side as i dont know how to extend this model using Algebra. Do you guys know how to tackle the part B of the question and any ideas on what models i can use?Name:  sequence screenshot.jpg
Views: 191
Size:  227.2 KB
This is quite an open-ended question; here are a few suggestions:

(a) What do you think a reasonable relationship between number of bacteria and area covered by the bacteria could be? Keep it simple!

(b) You've got a replication rate that doubles every time period. In other words, N_{t+1} = 2 \times N_{t} where N_{t} is the number at time t, with N_{0} = 2. What happens if you replace that 2 by something else?

(c) Same setup as part (b), but what if N_{0} is something different?

(d) This is the really interesting bit! Instead of N_{t+1} = 2 \times N_{t}, you've got to think of equations that include a term that reduces the rate of growth. Think how build up of waste products may be related to population size and how this may affect the growth rate of the current population. What would be a reasonable equation to summarize your findings?

Part (d) is very open-ended. If you want some inspiration, take a look at the Wikipedia article for "Population Dynamics", especially the bit about discrete time logistical models.
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Jyashi
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(Original post by Gregorius)
This is quite an open-ended question; here are a few suggestions:

(a) What do you think a reasonable relationship between number of bacteria and area covered by the bacteria could be? Keep it simple!

(b) You've got a replication rate that doubles every time period. In other words, N_{t+1} = 2 \times N_{t} where N_{t} is the number at time t, with N_{0} = 2. What happens if you replace that 2 by something else?

(c) Same setup as part (b), but what if N_{0} is something different?

(d) This is the really interesting bit! Instead of N_{t+1} = 2 \times N_{t}, you've got to think of equations that include a term that reduces the rate of growth. Think how build up of waste products may be related to population size and how this may affect the growth rate of the current population. What would be a reasonable equation to summarize your findings?

Part (d) is very open-ended. If you want some inspiration, take a look at the Wikipedia article for "Population Dynamics", especially the bit about discrete time logistical models.
Wow thanks a lot that suddenly made a lot of sense to me and also thank you for the link. I'll try to come up with different models and post back here to get feedback about it.
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