The formula R=-0.075 t 3.85 can be used to predict the world record in the 1500 meter run, t years after 1930.Determine an inequality that identifies the years in which the world record will be less than 3.1 minutes.
When the world record is less than 3.1, R is less than 3.1.
3.1 = -0.075t + 3.85
Solve for t (in years after 1930).
To determine the years in which the world record will be less than 3.1 minutes, we need to substitute the given value of 3.1 minutes into the formula and solve for t.
The formula R = -0.075t + 3.85 represents the world record in the 1500 meter run t years after 1930.
Substituting 3.1 for R, the formula becomes:
3.1 = -0.075t + 3.85
Now, let's rearrange the equation to isolate t:
-0.075t = 3.1 - 3.85
-0.075t = -0.75
To solve for t, we can divide both sides of the equation by -0.075:
t = (-0.75) / (-0.075)
t = 10
So, according to the formula, the world record will be less than 3.1 minutes 10 years after 1930.
However, keep in mind that we need to determine an inequality to identify the range of years in which the world record will be less than 3.1 minutes. As the formula gives us an equal sign, we can modify it into an inequality by using either "less than" (<) or "less than or equal to" (≤) signs.
Since we want to find the years when the record will be "less than" 3.1 minutes, the inequality can be written as:
t < 10
This means that the range of years in which the world record will be less than 3.1 minutes is any year before 10 years after 1930.