Question

The world record time for a certain swimming event was 63.2 seconds in 1950. Each year thereafter, the world record time decreased by 0.4 second
(a) Use a formula to express the world record time as a function of the time since 1950. (Lett be the time in years since 1950 and R the record time in seconds)
R
(6) Express using functional notation the world record time in the year 1957
RO
Calculate the world record time in the year 1957.
sec

Answer 1

Answer:

Let's define the variable t as the number of years that have passed since 1950.

Such that x = 0 represents the year 1950.

We know that in 1950, the record was 63.2 seconds.

And since each year since, the record has decreased by 0.4 seconds.

So we have a linear relationship:

R(t) = 63.2 s - 0.4s*t

When we have t = 0 (the year 1950)

The record is:

R(0) = 63.2s - 0.4s*0 = 63.2s

That is what we should expect.

Now, if t = 0 is the year 1950

Then t = 7 is the year 1957.

So the record in the year 1957 will be:

R(7) = 63.2s - 0.4s*7 = 60.4 seconds.