The mass in grams of the human brain during the last trimester and the first two

Question

The mass in grams of the human brain during the last trimester and the first two years after birth can be approximated by m(c)=0.01c^3-1500/c, where c is the head's circumference in centimeters. Find the average rate of change of m with respect to c The mass in grams of the human brain during the last trimester and the first two years after birth can be approximated by m(c)=0.01c^3-1500/c, where c is the head's circumference in centimeters. Find the average rate of change of m with respect to c from c = 30 cm to c = 50 cm. Include the units in your answer.from c = 30 cm to c = 50 cm. Include the units in your answer.

Explanation / Answer

Given: m(c) = 0.1c3 - 1500/c

m(30) = 0.01(30)3 - 1500/30 = 220gm

and m(50) = 0.01(50)3 - 1500/50 = 1220 gm

delta (m) = m(50) - m(30) = 1220 - 220 = 1000gm

delta (c) = 50 - 30 = 20 cm

Therefore, avaerage rate of change = delta (m)/delta (c)

= 1000 gm / 20 cm

= 50 gm/cm

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