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 is new to the team, so she starts 10 yards ahead of the starting line. nancy runs 6 yards per second.
describe the initial value of the function that represents paula’s run.
the initial value is 0. it represents paula’s distance from the start
paula:
time (seconds), x | 0 | 10 | 20
distance (yards), y | 0 | 70 | 140
describe the initial value of the function that represents nancy’s run.
the initial value is . it means that nancy ?

Explanation:

Step1: Understand Initial Value

The initial value of a function (for time - distance) is at \(x = 0\) (time = 0 seconds). For Nancy, we know she starts 10 yards ahead of the starting line. So when \(x = 0\) (at the start, time = 0), her distance \(y\) (from the starting line) is 10 yards.

Step2: Determine the Initial Value

The initial value of the function representing Nancy's run (distance as a function of time) is the distance when time \(x = 0\). Since she starts 10 yards ahead, at \(x = 0\), \(y=10\). This initial value means Nancy's distance from the starting line at the start (time = 0) is 10 yards.

Answer:

The initial value is \(10\). It means that Nancy starts 10 yards ahead of the starting line.