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. neither a relation nor a function
b. both a relation and a function
c. a relation only
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).

In the case of bacterial replication, let's consider time (in minutes) as the input and the number of bacteria as the output.

Step2: Analyze the bacterial replication as a relation and function

• Relation: The situation relates time (input) to the number of bacteria (output), so it is a relation (since there is a mapping between time and number of bacteria).
• Function: For any given time \( t \) (input), there is exactly one number of bacteria (output) because the replication follows a definite pattern (replicates every 14 minutes, so we can model the number of bacteria as a function of time, e.g., exponential growth \( N(t)=N_0 \cdot 2^{\frac{t}{14}} \) where \( N_0 \) is the initial number of bacteria). So each time \( t \) has exactly one corresponding number of bacteria, meaning it is a function.

Since it is both a relation (because it relates two quantities) and a function (because each input has exactly one output), the situation represents both a relation and a function.

Answer:

B. both a relation and a function