If the formula R = -0.037t + 50.1 can be used to predict the world record in the 400 meter dash t years after 1925, for what years will the world records be 48.1 seconds or less?
R = -0.037t + 50.1 <= 48.1
-0.037t <= -2
t >= 54.05
So, we need to be at least 55 years after 1925, or 1980.
In fact, according to the livestrong web site:
The International Association of Athletics Federation first recognized the 400-meter dash record in 1900, when it was set by the United States' Maxey Long in 47.8 seconds.
To determine the years when the world record in the 400-meter dash will be 48.1 seconds or less, we need to substitute the given value of 48.1 for R in the equation R = -0.037t + 50.1 and solve for t.
The equation R = -0.037t + 50.1 represents a linear relationship between the year (t) and the record time (R). The coefficient of t (-0.037) represents the rate of change of the record time per year.
Let's substitute R = 48.1 into the equation and solve for t:
48.1 = -0.037t + 50.1
To isolate the variable t, we subtract 50.1 from both sides of the equation:
48.1 - 50.1 = -0.037t
-2 = -0.037t
Next, divide both sides of the equation by -0.037 to solve for t:
-2 / -0.037 = t
Simplifying further:
t ≈ 54.05
Therefore, the world record in the 400-meter dash will be 48.1 seconds or less in approximately 54.05 years after 1925.
To find the specific year, we add the value of t (54.05) to 1925:
1925 + 54.05 ≈ 1979.05
So, the world record in the 400-meter dash will be 48.1 seconds or less in the year 1979 or 1980 (approximately).