maths help with geometric questions

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laura273
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Table shows the number of bacteria present in a particular sample for the first 5 minutes

For one strain of bacteria, each bacterium divides into two every minute.

Time Bacteria present
0 2
1 4
2 8
3 16
4 32
5 64

Note: The 0,1,2,3,4,5 is time and other figures are bacteria. I couldn't make a table properly.

Write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.
Write down an expression for the number of bacteria present after t minutes
Calculate the number of bacteria present after 2 hours. (State any assumptions you make.)
Calculate the time for the colony to reach 1 million bacteria.

Part B

Use algebra to extend this model for the growth of bacteria colonies.

You could investigate:

The relationship between the number of bacteria and the size of the colony
Different rates of replication
Colonies of different sizes at the start
Effect of growth limiting factors (such as build-up of waste products, competition for space)
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username3249896
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 U_n = ar^{n-1}
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laura273
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thanks but how do i apply it to the questions. please help me !
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username3249896
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(Original post by laura273)
thanks but how do i apply it to the questions. please help me !
a is the first term
n here is the time
r is the common ratio
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Muttley79
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(Original post by laura273)
thanks but how do i apply it to the questions. please help me !
We are not going to do your work for you - what have you done so far?
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Muttley79
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(Original post by BobbJo)
....
Please read the rules - we do not do people's work for them - I've mentioned this to you before.
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Muttley79
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(Original post by BobbJo)
a is the first term
Please stop ....
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laura273
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(Original post by BobbJo)
a is the first term
n here is the time
r is the common ratio
thanks but i know that part already. i am confused on part B
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username3249896
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(Original post by laura273)
thanks but i know that part already. i am confused on part B
after 0 minutes, the number is 2
after 1 minutes, the number is 4
after 2 minutes, the number is 8
after 3 minutes, the number is 16
so after t minutes it is?

use the formula  U_n= ar^{n-1} if you can't see it

a is the first term
n here is the time
r is the common ratio
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laura273
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(Original post by BobbJo)
after 0 minutes, the number is 2
after 1 minutes, the number is 4
after 2 minutes, the number is 8
after 3 minutes, the number is 16
so after t minutes it is?

use the formula  U_n= ar^{n-1} if you can't see it

a is the first term
n here is the time
r is the common ratio
i know how to do the first part, it part b that im struggling with.

Part B

Use algebra to extend this model for the growth of bacteria colonies.

You could investigate:

The relationship between the number of bacteria and the size of the colony
Different rates of replication
Colonies of different sizes at the start
Effect of growth limiting factors (such as build-up of waste products, competition for space)


i really apprecite you trying to help me!
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username3249896
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(Original post by laura273)
i know how to do the first part, it part b that im struggling with.

Part B

Use algebra to extend this model for the growth of bacteria colonies.

You could investigate:

The relationship between the number of bacteria and the size of the colony
Different rates of replication
Colonies of different sizes at the start
Effect of growth limiting factors (such as build-up of waste products, competition for space)


i really apprecite you trying to help me!

In part A, the formula for number of bacteria N at time t is  N = 2 \times 2^{t}

Apply this knowledge in part B,

The relationship between the number of bacteria and size of colony is simply that the greater the number of bacteria the greater the size of the colony.

If the rate of replication was different, e.g the number tripled every minute, how does the formula change?

If the initial size is different, how does the formula change?

If there is a limit on the overall growth, your formula must tend to a limit. How can you introduce a limit? [Hint:  1-e^{-t} tends to 1 as t tends to infinity]
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laura273
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(Original post by BobbJo)
In part A, the formula for number of bacteria N at time t is  N = 2 \times 2^{t}

Apply this knowledge in part B,

The relationship between the number of bacteria and size of colony is simply that the greater the number of bacteria the greater the size of the colony.

If the rate of replication was different, e.g the number tripled every minute, how does the formula change?

If the initial size is different, how does the formula change?

If there is a limit on the overall growth, your formula must tend to a limit. How can you introduce a limit? [Hint:  1-e^{-t} tends to 1 as t tends to infinity]
thanks so much! it makes so much more sense to me now
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pooja22
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(Original post by laura273)
Table shows the number of bacteria present in a particular sample for the first 5 minutes

For one strain of bacteria, each bacterium divides into two every minute.

Time Bacteria present
0 2
1 4
2 8
3 16
4 32
5 64

Note: The 0,1,2,3,4,5 is time and other figures are bacteria. I couldn't make a table properly.

Write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.
Write down an expression for the number of bacteria present after t minutes
Calculate the number of bacteria present after 2 hours. (State any assumptions you make.)
Calculate the time for the colony to reach 1 million bacteria.

Part B

Use algebra to extend this model for the growth of bacteria colonies.

You could investigate:

The relationship between the number of bacteria and the size of the colony
Different rates of replication
Colonies of different sizes at the start
Effect of growth limiting factors (such as build-up of waste products, competition for space)

Hey i how do you workout what expressioin to use for the number of bacteria present after t minute? oh this question is part a

xx
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RDKGames
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(Original post by pooja22)
Hey i how do you workout what expressioin to use for the number of bacteria present after t minute? oh this question is part a

xx
Either the question tells you explicitly, or you can just notice it from the data!

The no. of bacteria gets doubled after each equal interval of time, so this is this practically screaming geometric progression. And you should have a general expression you use for such progression.
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pooja22
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yes and for the i) part i answered with If B = the number of bacteria present
And t = time (Minutes)

Therefore, B = 2^t+1

but not entirely sure about what to answer for an expression for the number of bacteria present after t minutes. i just dont understand what the difference between i) and ii).
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RDKGames
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(Original post by pooja22)
yes and for the i) part i answered with If B = the number of bacteria present
And t = time (Minutes)

Therefore, B = 2^t+1

but not entirely sure about what to answer for an expression for the number of bacteria present after t minutes. i just dont understand what the difference between i) and ii).
In part (i) they are asking for the "algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously."
So really, the question asks what happens to the number of bacteria when going from one minute to the next. This is just a simple answer of "the number doubles".

Now part (ii) wants you to use this answer from part (i) and actually come up with a formula for the number of bacteria at time t, which is exactly what you got: B = 2^{t+1} (at least, I hope you don't mean B = 2^t + 1)
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pooja22
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(Original post by RDKGames)
In part (i) they are asking for the "algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously."
So really, the question asks what happens to the number of bacteria when going from one minute to the next. This is just a simple answer of "the number doubles".

Now part (ii) wants you to use this answer from part (i) and actually come up with a formula for the number of bacteria at time t, which is exactly what you got: B = 2^{t+1} (at least, I hope you don't mean B = 2^t + 1)
thank you so much for your help!!!
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pooja22
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(Original post by BobbJo)
In part A, the formula for number of bacteria N at time t is  N = 2 \times 2^{t}

Apply this knowledge in part B,

The relationship between the number of bacteria and size of colony is simply that the greater the number of bacteria the greater the size of the colony.

If the rate of replication was different, e.g the number tripled every minute, how does the formula change?

If the initial size is different, how does the formula change?

If there is a limit on the overall growth, your formula must tend to a limit. How can you introduce a limit? [Hint:  1-e^{-t} tends to 1 as t tends to infinity]
sorry can someone show me how the formula would change if it had tripled. im a bit daft so its taking me a while to figure it out.
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