Questions: The average person takes 10,000 steps in a day.

Solution Steps

To determine whether the function is linear or exponential and whether it is discrete or continuous, we need to analyze the nature of the data or function. A linear function has a constant rate of change, while an exponential function has a rate of change that is proportional to its current value. Discrete data consists of distinct, separate values, while continuous data can take any value within a range.

The average person takes \( 10,000 \) steps in a day. Since the number of steps taken can be modeled as a function where the rate of change is constant, we classify this function as linear. This can be expressed mathematically as:

\[ f(x) = mx + b \]

where \( m \) is the constant rate of change (steps per unit time) and \( b \) is the initial value.

The data representing the number of steps taken is countable and distinct, meaning it can only take on whole number values (e.g., \( 0, 1, 2, \ldots, 10,000 \)). Therefore, we classify this data as discrete.

Final Answer