Question

the table shows the world record times for the mens 50 meter breaststroke since 1995.
the equation ( y = - 0.109x + 244.607 ) models the relationship between ( x ), the year of the record, and ( y ), the world record time.
based on this model, what is the predicted world record time for the mens 50 meter breaststroke in the year 2020?
interpret your prediction in the context of the data.
when will the world record time for the mens 50
interpret your prediction in the context of the data.

Explanation:

Step1: Substitute the year into the equation

We need to find the value of \(y\) when \(x = 2020\). Substitute \(x=2020\) into the equation \(y=- 0.109x + 244.607\).
So, \(y=-0.109\times2020 + 244.607\).

Step2: Calculate the value of \(y\)

First, calculate \(-0.109\times2020=-0.109\times(2000 + 20)=-0.109\times2000-0.109\times20=-218-2.18=-220.18\).
Then, \(y=-220.18+244.607 = 24.427\approx24.4\).

Answer:

In the year 2020, the predicted record time will be 24.4 seconds.