Nitroglycerin is often prescribed to enlarge blood vessels that have become too constricted. If the cross-sectional area of a blood vessel t hours after nitroglycerin is administered is A (t) = 0.01t2 square centimeters (for 1 ≤ t ≤ 5), find the instantaneous rate of change of the cross-sectional area 3 hours after the administration of nitroglycerin.

Question

Mathematics

Hugh Bartlett

22 November, 11:54

Nitroglycerin is often prescribed to enlarge blood vessels that have become too constricted. If the cross-sectional area of a blood vessel t hours after nitroglycerin is administered is A (t) = 0.01t2 square centimeters (for 1 ≤ t ≤ 5), find the instantaneous rate of change of the cross-sectional area 3 hours after the administration of nitroglycerin.

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Yosef Key · Answer 1

Answer: 0.09 square centimiters

Step-by-step explanation:

Hi, to answer this question we have to solve the equation for t=3 hours.

A (t) = 0.01t2

Since t is the time in hours, For 3 hours, we simply have to replace the value of t by the number 3.

A (3) = 0.01 (3) ^2

A (3) = 0.01 (9)

A (3) = 0.09 square centimeters

the instantaneous rate of change of the cross-sectional area 3 hours after the administration of nitroglycerin is 0.09 square centimeters

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