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

Explanation:

Step1: Define relation and function

A relation is a set of ordered pairs \((x, y)\) where \(x\) and \(y\) are related in some way. A function is a special type of relation where each input \(x\) has exactly one output \(y\) (i.e., no two ordered pairs have the same \(x\)-value with different \(y\)-values).

Step2: Analyze the bacteria situation

Let \(x\) be the time (in minutes) and \(y\) be the number of bacteria. The number of bacteria at time \(x\) depends on \(x\) (since it replicates every 14 minutes, we can model it with an exponential function, e.g., \(y = N_0 \cdot 2^{\frac{x}{14}}\) where \(N_0\) is the initial number of bacteria).

• For any time \(x\), there is exactly one number of bacteria \(y\) (so it's a function).
• Since a function is a type of relation (because it's a set of ordered pairs \((x, y)\) with the function rule), it is also a relation. So the situation represents both a relation and a function.

Answer:

C. both a relation and a function