Respuesta :
Answer:
The linear model is;
[tex]f(t)=-0.005t+3.91[/tex]Explanation:
Given;
- In 1960, the world record for the men's mile was 3.91 minutes.
- In 1980, the record time was 3.81 minutes.
We want to write a linear model to represent the world record.
The linear model can be written in the form;
[tex]f(t)=mt+b[/tex]Where;
f(t) is the record for men's mile.
m and b are constant
t is the number of years since 1960.
At time t = 0, (year 1960)
[tex]\begin{gathered} f(t)=0+b \\ b=f(t)=3.91\text{ minutes} \\ b=3.91 \end{gathered}[/tex]Then the slope m will be;
[tex]\begin{gathered} m=\frac{\Delta f(t)}{\Delta t}=\frac{3.81-3.91}{1980-1960} \\ m=\frac{-0.1}{20} \\ m=-0.005 \end{gathered}[/tex]so, the linear model f(t) will be;
[tex]\begin{gathered} f(t)=mt+b \\ f(t)=-0.005t+3.91 \end{gathered}[/tex]Therefore, the linear model is;
[tex]f(t)=-0.005t+3.91[/tex]