Answer
(a)The slope is $0.0417D=0.0417*200=8.34$
and it represents how much the recommended child dosage increases for each year the child ages.
(b)The newborn dosage is $0.0417D=0.0417*200=8.34$ mg.
Work Step by Step
(a) We have $c=0.0417D(a+1).$ Multiplying the bracket:
$$c=0.0417Da+0.0417D.$$
Here the variable is the age of the child $a$ so the slope is everything that multiplies it i.e.
$$0.0417D.$$
The slope represents how much the recommended child dosage increases for each year the child ages.
(b) The newborn is zero years old so we put $a=0$ to get the recommended newborn dosage:
$$c_0=0.0417D(0+1)=0.0417D.$$
