Question

the table shows the world record times for the mens 50 meter breaststroke since 1995.
the equation ( y = - 0.109 x + 244.607 ) models the relationship between ( x ), the year of the record, and ( y ), the world record time (in seconds).
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 meter breaststroke reach 20 seconds?
interpret your prediction in the context of the data.

Explanation:

Step1: Predict for 2020

For the year 2020, \(x = 2020 - 1995=25\).
Substitute \(x = 25\) into the equation \(y=-0.109x + 24.607\).
\(y=-0.109\times25+24.607\)
\(y=-2.725 + 24.607\)
\(y = 21.882\)

Step2: Find when \(y = 20\)

Set \(y = 20\) in the equation \(y=-0.109x + 24.607\).
\(20=-0.109x + 24.607\)
\(0.109x=24.607 - 20\)
\(0.109x=4.607\)
\(x=\frac{4.607}{0.109}\approx42.27\)
The year is \(1995 + 42.27\approx2037\)

Answer:

• For 2020: The predicted world record time is approximately \(21.88\) seconds. This means that according to the linear model, in the year 2020, the men's 50 - meter breaststroke world record time is expected to be about \(21.88\) seconds.
• When \(y = 20\): The world record time for the Men's 50 - meter breaststroke will reach 20 seconds around the year 2037. This implies that as per the given linear relationship between the year and the record time, in approximately 2037, the record will be 20 seconds.