Table shows the number of bacteria present in a particular sample for the first 5 minutes
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 1 minute previously?
For the first question do i simply write a(r)^n. I know how to do geomectric sequences but i don't know in which format to link it with the bacteria number present one minute previously.
2. Write down an expression for the number of bacteria present after t minutes?
Can this simply just be f(t) = a(r)^t ?
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Jyashi
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- 29-10-2015 13:37
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- 29-10-2015 13:46
(Original post by Jyashi)
Table shows the number of bacteria present in a particular sample for the first 5 minutes
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 1 minute previously?
For the first question do i simply write a(r)^n. I know how to do geomectric sequences but i don't know in which format to link it with the bacteria number present one minute previously.
2. Write down an expression for the number of bacteria present after t minutes?
Can this simply just be f(t) = a(r)^t ?
For the first one you could maybe write it as a recurrence relation.
So N_(t+1) =2N_t. This would seem the best way of doing it to me. I know it isn't an explicitly defined sequence but it is still an algebraic rule right. -
Kevin De Bruyne
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- 29-10-2015 13:49
(Original post by Jyashi)
Table shows the number of bacteria present in a particular sample for the first 5 minutes
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 1 minute previously?
For the first question do i simply write a(r)^n. I know how to do geomectric sequences but i don't know in which format to link it with the bacteria number present one minute previously.
2. Write down an expression for the number of bacteria present after t minutes?
Can this simply just be f(t) = a(r)^t ?
For Q2 - I suppose you could have it of the form a(r)^ (t) or look at what the value of a is and simplify it. -
Jyashi
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- 29-10-2015 13:51
(Original post by B_9710)
for the second one you actually have to say what the constant A is - so you can actually work out the number of bacteria at t minutes. You know that A=2 since when t=0 the number of bacteria = 2
For the first one you could maybe write it as a recurrence relation.
So N_(t+1) =2N_t. This would seem the best way of doing it to me. I know it isn't an explicitly defined sequence but it is still an algebraic rule right.
For the recurrence sequence shouldnt it be a_t-1 instead of a_n-t ? -
Jyashi
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- 29-10-2015 13:55
(Original post by SeanFM)
For Q1 - if x is the number of bacteria present in a given minute, how many will there be in the next minute?
For Q2 - I suppose you could have it of the form a(r)^ (t) or look at what the value of a is and simplify it.
So for Q1 do you mean i should do it like this:
a(1) = 2
a(2) = 2(2)^2
a(3) = 2(2)^3
a(4) = 2(2)^4
a(5) = 2(2)^5
Should this suffice as a good answer for Q1? -
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- 29-10-2015 13:59
(Original post by Jyashi)
Thank you for your answer.
So for Q1 do you mean i should do it like this:
a(1) = 2
a(2) = 2(2)^2
a(3) = 2(2)^3
a(4) = 2(2)^4
a(5) = 2(2)^5
Should this suffice as a good answer for Q1?
If I told you that 'x' was the number of bacteria present at time t-1, what would be the number present at time t?
If you phrased that as an answer then I hope that it would suffice!
Or you could set up a recurrence relation, so f(t) = (relationship between f(t-1) and f(t) * f(t-1) for t greater than or equal to 1.Last edited by Kevin De Bruyne; 29-10-2015 at 14:03. -
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- 29-10-2015 15:36
(Original post by Jyashi)
Thank you for your answer.
For the recurrence sequence shouldnt it be a_t-1 instead of a_n-t ?Last edited by B_9710; 29-10-2015 at 15:37.
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