The question is asking me to use and inequality and the five step process to solve I get to a certain point and then I am stuck

Question

If the formula R = -0.037 + 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 record be 48.5 seconds or less?

 

R= -0.037 + 50.1

1. R= 49.973 but where to from here

Answer 1

Hi, Cynthia! You made two errors here, but only one of them is significant. The formula should be R=-0.037t + 50.1, where t is the number of years after 1925. So, let's start with the target time of 48.5 seconds.

We are looking for those years when the record time is 48.5 seconds or less:

48.5>-0.037t + 50.1

This will show us the first year when the record was LESS than 48.5, so we'll then find if the record was ever EXACTLY 48.5 seconds. Of course, the record was always less than 48.5 seconds in subsequent years;

1. Solve for t using algebraic methods:

2. 48.5-50.1>-0.037t

3. -1.6>-0.037t

4. -1.6/-0.037>t

Thus, 43.243...>t

This means the 43rd year is less than t & the 44th year is greater than t, so we reject the 43rd year as not meeting the criterion. According to this formula, the record was never exactly 48.5 seconds.

5. We add 44 years to 1925 to find the first year when the record fell below 48.5:

1925+44=1969. The record then continued to be broken each year afterward.

Your other mistake was an insignificant arithmetic error:

-0.037+50.1=50.063.

I hope this explanation helps you learn how to solve this type of problem. Good luck!