f(x)= 10.2217-0.0098x. f = the finishing time in the 100m dash and x is the number of years since 1960

Question

Interpret the y intercept
The model suggests that the finishing time in the 100m dash in 1960 was ___ seconds
Interpret the slope
The finishing time since 1960 has decreased each year by ___
The games where the 100 m dash is run occurs every 4 years. By how many seconds does the model predict the first place time will decrease every 4 years ____

Answer 1

To interpret the function \( f(x) = 10.2217 - 0.0098x \):

Y-Intercept Interpretation

The y-intercept occurs when \( x = 0 \): \[ f(0) = 10.2217 - 0.0098(0) = 10.2217 \] This means that the model suggests that the finishing time in the 100m dash in 1960 was 10.2217 seconds.

Slope Interpretation

The slope of the function is \( -0.0098 \). This means that the finishing time in the 100m dash has decreased each year by 0.0098 seconds. This indicates an annual improvement in the performance of the runners.

Prediction of First Place Time Decrease Every 4 Years

Since the games occur every 4 years, to find the total decrease over this time span, we can multiply the slope by 4: \[ \text{Decrease in 4 years} = 4 \times (-0.0098) = -0.0392 \] Thus, the model predicts that the first place time will decrease by 0.0392 seconds every 4 years.