World Records in the 1500-m Run. The formula R = -0.075t + 3.85 can be used to predict the world record in the 1500-m run t years after 1930. Determine (in terms of an inequality) those years for which the world record will be less than 3.5 min.
{ Y l Y > 1930 } ?
you just need t where
-0.075t + 3.85 < 3.5
0.075t > 0.35
t > 4.67
So, any year after 1935
To determine the years for which the world record in the 1500-m run will be less than 3.5 minutes, we need to substitute 3.5 for R in the given formula and solve for t.
The formula R = -0.075t + 3.85 represents the predicted world record (in minutes) t years after 1930. Substituting 3.5 for R, we have:
3.5 = -0.075t + 3.85
To solve for t, we can start by isolating the variable on one side of the equation. Subtracting 3.85 from both sides gives:
-0.35 = -0.075t
To isolate t, divide both sides of the equation by -0.075:
t = -0.35 / -0.075
Simplifying the right side of the equation gives:
t ≈ 4.667
This means that the world record will be less than 3.5 minutes in the years after approximately 4.667 years (or 4 years and 8 months) after 1930.
Therefore, the inequality representing the years for which the world record will be less than 3.5 min is:
t > 4.667
In set-builder notation, the years for which the world record will be less than 3.5 minutes can be written as:
{ t | t > 4.667 }