The formula R= -0.75t +385
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 3.7 min. Solve for t
To determine the years for which the world record will be less than 3.7 minutes, we need to substitute the value of R (world record) into the given formula and solve for t.
Given formula: R = -0.75t + 385
Substituting R = 3.7 (world record in minutes) into the formula, we get:
3.7 = -0.75t + 385
Now, let's solve this equation to find the value of t:
3.7 - 385 = -0.75t
-381.3 = -0.75t
Dividing both sides of the equation by -0.75:
-381.3 / -0.75 = t
t ≈ 508.4
The value of t represents the number of years after 1930. To determine the years, we add t to the base year:
1930 + 508.4 ≈ 2438.4
Therefore, the world record will be less than 3.7 minutes for the years before approximately 2438.4. In terms of an inequality, it can be written as:
t < 2438.4