# Geometric sequence help!!!!

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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

1)write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.

(This I can do it's a geometric formula)

2) Write down an expression for the number of bacteria present after t minutes.

3) calculate the number of bacteria after 2 hours.(state any assumptions you can make)

4) calculate the time it takes for the colony to reach 1 million bacteria. ( Does this require logs and sum of series).

Any help would mean a lot.

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

1)write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.

(This I can do it's a geometric formula)

2) Write down an expression for the number of bacteria present after t minutes.

3) calculate the number of bacteria after 2 hours.(state any assumptions you can make)

4) calculate the time it takes for the colony to reach 1 million bacteria. ( Does this require logs and sum of series).

Any help would mean a lot.

Last edited by Thesleepystudent; 1 month ago

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(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

1)write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.

(This I can do it's a geometric formula)

2) Write down an expression for the number of bacteria present after t minutes.

Any help would mean a lot

**Thesleepystudent**)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

1)write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.

(This I can do it's a geometric formula)

2) Write down an expression for the number of bacteria present after t minutes.

Any help would mean a lot

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#3

If you just wrote down the powers of 2, up to 64 (2

^{6}), it might become obvious what the general rule is
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(Original post by

Instead of a term to term geometric relationship (part 1), what do you know about position to term geometric relationship? That's what you need for part 2.

**mqb2766**)Instead of a term to term geometric relationship (part 1), what do you know about position to term geometric relationship? That's what you need for part 2.

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(Original post by

If you just wrote down the powers of 2, up to 64 (2

**Sinnoh**)If you just wrote down the powers of 2, up to 64 (2

^{6}), it might become obvious what the general rule is
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#6

(Original post by

I understand the general rule is a geometric sequence however I'm unsure about question 2

**Thesleepystudent**)I understand the general rule is a geometric sequence however I'm unsure about question 2

(Original post by

Should I rearrange the equation to make t the subject so it is in the (Un= ) postion

**Thesleepystudent**)Should I rearrange the equation to make t the subject so it is in the (Un= ) postion

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#7

**Thesleepystudent**)

Should I rearrange the equation to make t the subject so it is in the (Un= ) postion

Un = 5 + 3(n-1)

Where 5 is the initial value and 3 the common difference.

For a geometric sequence it's

Un = a*r^(n-1)

So identify the initial value "a" and the common ratio "r"

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(Original post by

If it was an arithmetic sequence you'd have something like

Un = 5 + 3(n-1)

Where 5 is the initial value and 3 the common difference.

For a geometric sequence it's

Un = a*r^(n-1)

So identify the initial value "a" and the common ratio "r"

**mqb2766**)If it was an arithmetic sequence you'd have something like

Un = 5 + 3(n-1)

Where 5 is the initial value and 3 the common difference.

For a geometric sequence it's

Un = a*r^(n-1)

So identify the initial value "a" and the common ratio "r"

(Original post by

All it's asking for is to write a function that tells you the number of bacteria at a given time. It'll have to be an exponential, and there would have to be a 2 as the basis of the exponent since it doubles at each minute.

That would give you the time elapsed for a given number of bacteria - they're asking for the opposite of that.

**Sinnoh**)All it's asking for is to write a function that tells you the number of bacteria at a given time. It'll have to be an exponential, and there would have to be a 2 as the basis of the exponent since it doubles at each minute.

That would give you the time elapsed for a given number of bacteria - they're asking for the opposite of that.

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#9

(Original post by

a=2 and r=2. n becomes t for the first half. However how could I find after t for the second half.

Thank you for your help so after t minute Un= 2^n+1 because each power goes up by 1 so if n =1 the answer will be 4.

**Thesleepystudent**)a=2 and r=2. n becomes t for the first half. However how could I find after t for the second half.

Thank you for your help so after t minute Un= 2^n+1 because each power goes up by 1 so if n =1 the answer will be 4.

*in terms of t*. Like, if N is the number of bacteria, then N = f(t).

But you're very close to the right answer.

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(Original post by

They want it

But you're very close to the right answer.

**Sinnoh**)They want it

*in terms of t*. Like, if N is the number of bacteria, then N = f(t).But you're very close to the right answer.

So far for part 1) 2*2^t-1= 2^t-1 we replace n with t because we're looking for the time(t) at a particular time.

Part 2) Ut= 2^t+1 the base will be 2 as the number of bacteria doubles each time with power going up by 1 each time.

And finally part 3) I just put 2 hours(120 seconds) into the equation in part 2 and not quite sure what I make assumptions on.

Thanks once again,

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#11

(Original post by

Thank you for the help could you check I'm on the right track. I feel like I'm a little off.

So far for part 1) 2*2^t-1= 2^t-1 we replace n with t because we're looking for the time(t) at a particular time.

Part 2) Ut= 2^t+1 the base will be 2 as the number of bacteria doubles each time with power going up by 1 each time.

And finally part 3) I just put 2 hours(120 seconds) into the equation in part 2 and not quite sure what I make assumptions on.

Thanks once again,

**Thesleepystudent**)Thank you for the help could you check I'm on the right track. I feel like I'm a little off.

So far for part 1) 2*2^t-1= 2^t-1 we replace n with t because we're looking for the time(t) at a particular time.

Part 2) Ut= 2^t+1 the base will be 2 as the number of bacteria doubles each time with power going up by 1 each time.

And finally part 3) I just put 2 hours(120 seconds) into the equation in part 2 and not quite sure what I make assumptions on.

Thanks once again,

The main assumption is that the number of bacteria grow without limit, continuing to double every minute - in practice they'd run out of space or food or die off. 2^119 is a pretty big number after all. That much bacteria would probably weigh as much as the Moon.

The question describes it as "bacteria present", so for 4) you don't need to interpret it as the sum of a series.

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