Question
f(x)= 10.2217-0.0098x. f = the finishing time in the 100m dash and x is the number of years since 1960
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 ____
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 ____
Answers
GPT-4o mini
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.
### 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.