Brightness of the star is given by, $\"\"$ .

Rate of change of change of function $\"\"$ is defined as $\"\"$ .

(a)

The rate of change of brightness after t days is given by,

$\"\"$

$\"\"$ .

(b)

The rate of increase of brightness after one day :

$\"\"$

Plug in $\"\"$ in above expression.

$\"\"$

The rate of increase of brightness after one day is 0.16.

(a) $\"\"$ .

(b) 0.16.