Question

The table shows the predicted growth of bacteria after various numbers of hours. Write an explicit formula for the number of bacteria after n hours.

Answer 1

The answer would be the second one, a_n=21n+8

Explanation:

If you plot all the points on a graph, you can then check the answers given.

Answer 2

`a_n=21n+8`

Explanation:

First we determine what type of sequence is represented in this table.

To get from the first term to the second term, 29 to 50, we add 21.

To get from the second term, 50, to the third term, 71, we add 21.

To get from the third term, 71, to the fourth term, 92, we add 21.

To get from the fourth term, 92, to the fifth term, 113, we add 21.

Since we add a constant to find the next term each time, this is an arithmetic sequence. The explicit formula for an arithmetic sequence is

`a_n=a_1+d(n-1)`, where a₁ is the first term and d is the common difference. For this sequence, it is

`a_n=29+21(n-1)`

To simplify this, first use the distributive property:

`a_n=29+21(n)-21(1)\\\\a_n=29+21n-21`

Combine like terms:

`a_n=29+21n-21\\\\a_n=21n+8`