Question

In 1960, the world record for the men's mile was 3.91 minutes. In 1980, the record time was 3.81 minutes. Write a linear model that represents the world record (in minutes) for the men's mile as a function of the number of years, t, since 1960.

Answer 1

The linear model is;

`f(t)=-0.005t+3.91`

Step-by-step 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;

`f(t)=mt+b`

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)

`\begin{gathered} f(t)=0+b \\ b=f(t)=3.91\text{ minutes} \\ b=3.91 \end{gathered}`

Then the slope m will be;

`\begin{gathered} m=(\Delta f(t))/(\Delta t)=(3.81-3.91)/(1980-1960) \\ m=(-0.1)/(20) \\ m=-0.005 \end{gathered}`

so, the linear model f(t) will be;

`\begin{gathered} f(t)=mt+b \\ f(t)=-0.005t+3.91 \end{gathered}`

Therefore, the linear model is;

`f(t)=-0.005t+3.91`