Question

The equation R= -0.028t +20.8 can be used to predict the world record in the 200 meter​ dash, where R stands for the record in seconds and t for the number of years since 1920. In what year did the record become 19.68 ​seconds?

Answer 1

1960

Explanation:

Given:

The equation to represent the world record in the 200 meter dash is given as:

`R=-0.028t+20.8\\Where\ R\to time\ in\ seconds\\t\to years\ since\ 1920`

Also, R = 19.68 s

So, we need to find the time in years when 'R' is 19.68 s.

As 't' represents the time in years since 1920, so for the year 1920, t = 0 and so on.

Now, plug in 19.68 for 'R' in the above equation and solve for 't'. This gives,

`19.68=-0.028t+20.8\\\\0.028t=20.8-19.68\\\\0.028t=1.12\\\\t=(1.12)/(0.028)\\\\t=40\ years\ since\ 1920`

Therefore, in order to get the year, we add 40 to 1920. This gives,

The record become 19.68 s in the year = 1920 + 40 = 1960