Question

select the correct answer.
a particular strain of a common bacteria replicates itself every 14 minutes. which of the following does this situation represent?
a. a relation only
b. both a relation and a function
c. neither a relation nor a function
d. a function only

Explanation:

Step1: Recall definitions of relation and function

A relation is a set of ordered pairs (or a mapping between two sets). A function is a special type of relation where each input (from the domain) has exactly one output (in the codomain).

Step2: Analyze the bacteria replication situation

Let's consider time (input) and the number of bacteria (output). For any given time \( t \) (in minutes, especially multiples of 14 for replication events, or even continuous time in a model), the number of bacteria is determined.

• As a relation: There is a mapping between time values and the number of bacteria (so it's a relation).
• As a function: For each time \( t \), there is exactly one number of bacteria (since the replication follows a rule, each time gives a unique count of bacteria). So it's also a function.

Answer:

B. both a relation and a function