Final answer:
The input variable of this function is time, t, in minutes.
Step-by-step explanation:
In the given context, the input variable of the function is time, denoted as 't' and measured in minutes. The distance walked, 'd,' is dependent on the time elapsed since the walk began. This relationship is expressed as a function where the input, 't,' influences the output, 'd,' indicating that as time progresses, the distance covered changes accordingly.
Understanding this requires recognizing that the function is specifically defined in terms of time, making it the independent variable. For example, if the function is represented as \(d(t)\), it signifies that the distance is a function of time. In mathematical terms, the input variable 't' is the domain of the function, representing all possible values of time during the walk.
To illustrate, if the function is \(d(t) = 5t\), where 5 is a constant representing the walking speed, it implies that the distance walked, 'd,' is directly proportional to the time, 't.' In this case, for every additional minute, the distance covered increases by 5 kilometers.
Understanding the nature of the input variable is crucial for interpreting and manipulating the function appropriately. It emphasizes that changes in distance are contingent on the duration of the walk, reinforcing the role of time as the driving factor in this particular mathematical relationship.