The formula R= -0.075t + 3.85 can be used to perdict 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 3.4 minutes.
Soleve for t.
t >__? round to the nearest whiole number.
-0.075t + 3.85 < 3.4
Change the < to = and solve the resulting equation to get the year (measured from 1930) that the world record will become 3.4 minutes.
To determine the years in which the world record will be less than 3.4 minutes, we need to substitute 3.4 for R in the given formula and solve for t. The formula we have is:
R = -0.075t + 3.85
Substituting 3.4 for R, we get:
3.4 = -0.075t + 3.85
To solve for t, we can isolate the t term by subtracting 3.85 from both sides of the equation:
3.4 - 3.85 = -0.075t
-0.45 = -0.075t
Now, we can solve for t by dividing both sides of the equation by -0.075:
-0.45 / -0.075 = t
6 = t
Therefore, t = 6 years. This means the world record will be less than 3.4 minutes 6 years after 1930.
To find the inequality that identifies the years, we know that t has to be greater than 6 since we are looking for years after 1930. To represent this as an inequality, we write:
t > 6
So, the inequality that identifies the years in which the world record will be less than 3.4 minutes is t > 6.