A rare bacterial culture is being grown in a lab. As time passes, the cells multiply in a specific pattern. 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. How many cells will there be after seven days?

a. 149B. 120C. 98D. 94

Question

Mathematics

Kane Perkins

10 February, 19:26

A rare bacterial culture is being grown in a lab. As time passes, the cells multiply in a specific pattern. 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. How many cells will there be after seven days?

a. 149B. 120C. 98D. 94

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Answers (1)

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Quincy · Answer 1

the equation is,

a_n = a_ (n-1) + 3 * n + 2

Substituting the values for day 4,

20 + 3*4 + 2 = 34

Thus the equation is correct

Therefore to calculate for a_n at n = 7 or a_7, we must calculate a_5 and a_6 first.

a_5 = 34 + 3*5 + 2 = 51

a_6 = 51 + 3*6 + 2 = 71

Hence,

a_7 = 71 + 3*7 + 2 = 94

Answer: D. 94