Question

14. 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.
Awhich recursive equation represents the pattern? (2 points)
an = an - 1 + 3n
an = an - 1 +n + 2)
an = an - 1 + 3(n + 2)
an = an - 1 + (3n + 2)

Answer 1

a[n] = a[n-1] +(3n +2)

Explanation:

The difference between Day 1 and Day 2 is 9 - 1 = 8 cells. The difference between a2 and a1 in each of the answer choices is a2 -a1 = ...

3n = 3(2) = 6 ≠ 8

n+2 = 2+2 = 4 ≠ 8

3(n+2) = 3(2+2) = 12 ≠ 8

3n +2 = 3(2) +2 = 8 . . . . . . this is the appropriate choice:

`\boxed{a_n=a_(n-1)+(3n+2)}`