A rare bacterial culture is being grown in a lab. As the days progress, the cells multiply and grow.
After 1 day, there is only 1 cell.
After 2 days, there are 9 cells.
After 3 days, there are 20 cells.
After 4 days, there are 34 cells.
Which recursive equation represents the pattern?
To find the recursive equation that represents the pattern, we need to analyze the given data and identify the relationship between the number of days and the number of cells.
In this case, we can observe that the number of cells is increasing with each passing day. Looking at the numbers, it seems that the increase in the number of cells is related to the previous day's number of cells.
Let's break it down:
After 1 day: 1 cell
After 2 days: 9 cells
The increase from day 1 to day 2 is 9 - 1 = 8 cells.
After 2 days: 9 cells
After 3 days: 20 cells
The increase from day 2 to day 3 is 20 - 9 = 11 cells.
After 3 days: 20 cells
After 4 days: 34 cells
The increase from day 3 to day 4 is 34 - 20 = 14 cells.
From this analysis, we can see that the number of cells is increasing by the same amount each day. This means that the increase is constant.
To find the recursive equation, we can express the number of cells on any given day (n) in terms of the number of cells on the previous day (n-1) and the constant increase (k).
Let's denote the number of cells on day n as C(n).
On day n, the number of cells (C(n)) is equal to the number of cells on the previous day (C(n-1) plus the constant increase (k):
C(n) = C(n-1) + k
In our case, the constant increase is the same: 8 cells, 11 cells, 14 cells, etc.
Therefore, the recursive equation that represents the pattern is:
C(n) = C(n-1) + k
where k is a constant that represents the increase in the number of cells from one day to the next.
What are your choices?
an=an-1+3n
an=an-1+(n+2)
an=an-1+3(n+2)
an=an-1+(3n+2)
I thought it was the last one but am not sure and am trying to help my grandson.
thank you
well, the amounts added are 8,11,14
They differ by 3, so it will look like
a(n) = a(n-1) + 3n + ?
3n looks like 3,6,9, so we have
a(n) = a(n-1) + 3(n-1)+5 = a(n-1)+(3n+2)
so you are correct