Question

paula and nancy race at track practice. paula records her time in a table where her distance in yards, y, is a function of her time in seconds, x. nancy runs 6 yards per second. nancy is new to the team, so she starts 10 yards ahead of the starting line.
describe the initial value of the function that represents paula’s run.
the initial value is \boxed{}. it represents paula’s ?

Explanation:

Step1: Understand Initial Value

The initial value of a function (when dealing with distance - time) is the value of the function when \(x = 0\) (time \(= 0\) seconds). For Paula's data, when \(x = 0\) (time \(= 0\) seconds), the distance \(y\) (from the table) is \(0\) yards. This initial value represents Paula's distance at the start of the run (when time is \(0\) seconds).

Step2: Confirm the Initial Value

Looking at the table for Paula: when \(x = 0\) (time in seconds is \(0\)), \(y = 0\) (distance in yards is \(0\)). So the initial value of Paula's distance - time function is \(0\), and it represents her starting distance (distance at time \(t = 0\)).

Answer:

The initial value is \(0\). It represents Paula's starting distance (distance at time \(t = 0\) seconds).