In 1920, the record for a certain race was 45.5 sec. In 1970, It was 44.5 sec. Let R(t)=the record in the race and t=the number of years since 1920 Predict the record for 2003 and 2006

To predict the record for 2003 and 2006, we can use the given data and assume a linear relationship between the record time and the number of years since 1920.

Let's start by finding the rate of change of the record time over the years. The record time in 1970 is 44.5 seconds, and the record time in 1920 is 45.5 seconds. So, the change in the record time over 50 years is:

Change in record time = 44.5 seconds - 45.5 seconds = -1 second

Since this change occurred over 50 years, we can find the rate of change per year:

Rate of change = Change in record time / Number of years = -1 second / 50 years

Now, let's use this rate of change to predict the record time for 2003 and 2006.

For 2003 (t = 2003 - 1920 = 83 years), we can use the formula:

R(t) = R(0) + Rate of change * t

R(83) = 45.5 seconds + (-1 second / 50 years) * 83 years

Simplifying this equation, we get:

R(83) = 45.5 seconds - (83/50) seconds

R(83) ≈ 44.82 seconds

Therefore, we can predict the record for 2003 to be approximately 44.82 seconds.

Similarly, for 2006 (t = 2006 - 1920 = 86 years), the formula becomes:

R(86) = 45.5 seconds + (-1 second / 50 years) * 86 years

Simplifying this equation, we get:

R(86) = 45.5 seconds - (86/50) seconds

R(86) ≈ 44.92 seconds

Therefore, we can predict the record for 2006 to be approximately 44.92 seconds.