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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)

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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#4

(Original post by

thanks but how do i apply it to the questions. please help me !

**laura273**)thanks but how do i apply it to the questions. please help me !

n here is the time

r is the common ratio

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#5

(Original post by

thanks but how do i apply it to the questions. please help me !

**laura273**)thanks but how do i apply it to the questions. please help me !

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#6

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....

**BobbJo**)....

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#9

(Original post by

thanks but i know that part already. i am confused on part B

**laura273**)thanks but i know that part already. i am confused on part B

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 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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(Original post by

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 if you can't see it

a is the first term

n here is the time

r is the common ratio

**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 if you can't see it

a is the first term

n here is the time

r is the common ratio

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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#11

(Original post by

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!

**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

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: tends to 1 as t tends to infinity]

Last edited by username3249896; 2 years ago

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(Original post by

In part A, the formula for number of bacteria N at time t is

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: tends to 1 as t tends to infinity]

**BobbJo**)In part A, the formula for number of bacteria N at time t is

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: tends to 1 as t tends to infinity]

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#13

(Original post by

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)

**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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#14

(Original post by

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

**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

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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#15

*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).

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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#16

(Original post by

And t = time (Minutes)

**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).***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 , which is exactly what you got: (at least, I hope you don't mean )

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#17

(Original post by

In part (i) they are asking for the "algebraic rule linking the number of bacteria

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 , which is exactly what you got: (at least, I hope you don't mean )

**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 , which is exactly what you got: (at least, I hope you don't mean )

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#18

**BobbJo**)

In part A, the formula for number of bacteria N at time t is

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: tends to 1 as t tends to infinity]

0

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