The daily quantity π, in milli grams, of medication is determined by the age π
,in years, of a patient, so π=π(π).
Suppose we are told
(a) π(30)=150
(b) πβ²(30)=5.8
Estimate the daily dose of medication, in milli grams, for a patient who is 34 years old.
We can use linear approximation to estimate the daily dose of medication for a patient who is 34 years old:
Let π₯ = 34, π₯0 = 30, and Ξπ₯ = π₯ - π₯0 = 4.
Then, by linear approximation:
π(π₯) β π(π₯0) + πβ²(π₯0)(Ξπ₯)
π(34) β π(30) + πβ²(30)(4)
π(34) β 150 + 5.8(4)
π(34) β 172.2
Therefore, the estimated daily dose of medication for a patient who is 34 years old is 172.2 milligrams.