please help me solve this problem.
The formula R=0.075 + 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 3.7. Solve for t.
Thanks
To determine the years in which the world record will be less than 3.7, we need to set up an inequality using the given information.
The formula R = 0.075t + 3.85 represents the world record t years after 1930.
To find when the world record is less than 3.7, we set up the inequality:
0.075t + 3.85 < 3.7
To solve for t, we need to isolate it on one side of the inequality. Let's now go through the steps to solve for t:
1. Subtract 3.85 from both sides of the inequality:
0.075t + 3.85 - 3.85 < 3.7 - 3.85
0.075t < -0.15
2. Divide both sides of the inequality by 0.075 to isolate t:
(0.075t) / 0.075 < (-0.15) / 0.075
t < -2
Therefore, the inequality that identifies the years in which the world record will be less than 3.7 is t < -2. This means that any time before 1930 - 2 years (or 1928 in this case), the world record will be less than 3.7.
However, since we are looking for years after 1930, we need to consider the positive values of t. In this case, there are no positive values of t that satisfy the inequality t < -2. Therefore, there are no years after 1930 in which the world record will be less than 3.7 according to the given formula.