Science:Math Exam Resources/Courses/MATH102/December 2017/Question 14 (a)
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Question 14 (a)
The males of the magnificent frigatebirds have a bright red throat pouch that gets inflated like a balloon to attract females during mating season. Suppose that the rate of change of the volume during inflation is
measured in for . At , the pouch is empty.
(a) Find the function for the volume at time during inflation.
(Hint: consider a simple antiderivative.)
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The antiderivative of is .
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By the Hint, the antiderivative of is
where is an arbitrary constant.
this implies that
where is a constant.
As we are given that , we have