Women’s records in the women’s 1500-m run.
The formula R =−0.0026? + 4.0807 can be used to predict the world record, in minutes, for the 1500-m run t years after 1900. Determine (in terms of an inequality) those years for which the world record will be less than 3.8 min.
To determine the years for which the world record will be less than 3.8 minutes, we can use the given formula and solve for t when the record time is less than 3.8 minutes.
The formula given is:
R = -0.0026t + 4.0807,
where R represents the world record time in minutes and t represents the number of years after 1900.
To find the years when the world record is less than 3.8 minutes, we substitute R with 3.8 in the formula and solve for t:
3.8 = -0.0026t + 4.0807.
Rearranging the equation, we get:
-0.0026t = 3.8 - 4.0807,
-0.0026t = -0.2807.
To isolate t, we divide both sides of the equation by -0.0026:
t = (-0.2807) / (-0.0026).
Calculating this value, we find:
t ≈ 108.038,
where t is approximately 108.038 years.
To express this result in terms of an inequality, we want to find the years after 1900 when the world record will be less than 3.8 minutes. Therefore, the inequality we can use is:
t > 108.038.
In other words, any year (t) after approximately 108.038 years after 1900 will have a world record time for the 1500-m run that is less than 3.8 minutes.