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# Help understanding arithmetic and geometric sequence question? watch

1. 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 ?
2. (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 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.
3. (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 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.
4. (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 ?
5. (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?
6. (Original post by Jyashi)

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?
I too am a bit unsure about what they want as an algebraic rule, but I think you'd want it to be more general than that.

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.
7. (Original post by Jyashi)

For the recurrence sequence shouldnt it be a_t-1 instead of a_n-t ?
In the sequence I have given I let N be the number f bacteria and t be the time. So it just says that the nunber of bacteria after a minute is double the bacteria that there was in the previous minute.

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