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The observed rabbit population on an island is given by the function p(t) =-4t^2+80t+1200, where t is the time, in years, since the teachers began observing the rabbits. According to this quadratic function, after how many years will the rabbit population reach its peak

User Idaho
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1 Answer

4 votes

Answer:

The rabbit population will reach its peak after 10 years.

Explanation:

Suppose we have a quadratic function in the following format:


p(t) = at^(2) + bt + c

The vertex of the function is the point:


(t_(v), p(t_(v))

In which


t_(v) = -(b)/(2a)

If a is negative, the vertex is a peak.

In this question:


p(t) = -4t^(2) + 80t + 1200

So


a = -4, b = 80, c = 1200

According to this quadratic function, after how many years will the rabbit population reach its peak

This is
t_(v)


t_(v) = -(b)/(2a) = -(80)/(2*(-4)) = 10

The rabbit population will reach its peak after 10 years.

User Deepesh Thapa
by
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