The daily quantity 𝑄, in milli grams, of medication is determined by the age 𝑎

Question

The daily quantity 𝑄, in milli grams, of medication is determined by the age 𝑎

,in years, of a patient, so 𝑄=𝑓(𝑎).

Suppose we are told

(a) 𝑓(30)=150

(b) 𝑓′(30)=5.8

Estimate the daily dose of medication, in milli grams, for a patient who is 34 years old.

Answer 1

We can use linear approximation to estimate the daily dose of medication for a patient who is 34 years old:

Let 𝑥 = 34, 𝑥0 = 30, and Δ𝑥 = 𝑥 - 𝑥0 = 4.

Then, by linear approximation:

𝑓(𝑥) ≈ 𝑓(𝑥0) + 𝑓′(𝑥0)(Δ𝑥)

𝑓(34) ≈ 𝑓(30) + 𝑓′(30)(4)

𝑓(34) ≈ 150 + 5.8(4)

𝑓(34) ≈ 172.2

Therefore, the estimated daily dose of medication for a patient who is 34 years old is 172.2 milligrams.