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

Question

Hours 1,2,3,4,5
Number of bacteria 21, 42, 63, 84, 105
(1 point)
Responses

an=21n+21
A sub n is equal to 21 n plus 21

an= 1,21 n
A sub n is equal to 1 over 21 n

an=21n
A sub n is equal to 21 n

an=n+21
A sub n is equal to n plus 21

Answer 1

To find an explicit formula for the sequence of the number of bacteria at different hours, observe the pattern in the given numbers:

• At hour 1, there are 21 bacteria.
• At hour 2, there are 42 bacteria.
• At hour 3, there are 63 bacteria.
• At hour 4, there are 84 bacteria.
• At hour 5, there are 105 bacteria.

Let's look for a pattern:

• The number of bacteria increases by 21 for each additional hour:
  • From 21 to 42 (21)
  • From 42 to 63 (21)
  • From 63 to 84 (21)
  • From 84 to 105 (21)

We can observe that the number of bacteria can be expressed in terms of n, where n is the number of hours:

If we let \( n \) be the hour, we can express the number of bacteria as: \[ a_n = 21n \] This means that for every hour \( n \), the number of bacteria is 21 times \( n \).

Therefore, the explicit formula for the sequence of the number of bacteria is: \[ a_n = 21n \]

So the correct response is:

an = 21n
A sub n is equal to 21 n.