$\"\"$

(a)

The function is $\"\"$ , where $\"\"$ represents the year and $\"\"$ is the time in minutes and seconds.

First convert seconds to decimal parts of minutes.

Conversion from seconds to minutes :

$\"\"$

After conversion the table :

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Graph :

Draw a coordinate plane.

Plot the points obtained in the in the above table.

Connect those points with a smooth curve.

Graph of the function $\"\"$ : $\"\"$

$\"\"$

(b)

For 1 mile run there is no time limit.

So consider $\"\"$ .

Find $\"\"$ .

$\"\"$

Divide the numerator and denominator by $\"\"$ .

$\"\"$

The appearing time for running 1 mile is $\"\"$ .

Yes, there is a appearing time for running 1 mile.

The appearing limit time for running 1 mile is $\"\"$ .

$\"\"$

(a)

Graph of the function $\"\"$ : $\"\"$

(b)

Yes, the appearing limit time for running 1 mile is $\"\"$ .