## Calculus: Early Transcendentals 8th Edition

(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.
(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: $$c_0=0.0417D(0+1)=0.0417D.$$