Question

tutorial exercise
if the recommended adult dosage for a drug is ( d ) (in mg), then to determine the appropriate dosage ( c ) for a child of age ( a ), pharmacists use the equation ( c = 0.0417d(a + 1) ). suppose the dosage for an adult is 300 mg.
(a) find the slope of the graph of ( c ). what does it represent?
(b) what is the dosage for a newborn?
step 1
(a) find the slope of the graph of ( c ). what does it represent?
we are given ( d = 300 ). substitute 300 for ( d ) in the equation ( c = 0.0417d(a + 1) ). after simplifying, we get
( c = 0.0417(300)(a + 1) )
( = left( square
ight)a + square ).

Explanation:

Step1: Substitute D=300 into formula

$c = 0.0417(300)(a + 1)$

Step2: Calculate coefficient of a

$0.0417\times300 = 12.51$

Step3: Expand to slope-intercept form

$c = 12.51a + 12.51$

Step4: Identify slope and meaning

Slope = 12.51, it represents the rate of increase in child dosage per year of age.

Step5: Calculate newborn dosage (a=0)

$c = 12.51(0) + 12.51 = 12.51$

Answer:

(a) The slope is 12.51, representing the increase in child dosage (in mg) per additional year of age.
(b) The dosage for a newborn is 12.51 mg.
The simplified equation is $\boldsymbol{(12.51)a + 12.51}$