Question

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

Answer 1

Answer:

The rabbit population will reach its peak after 10 years.

Step-by-step 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

$t_{v} = -\frac{b}{2a}$

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 $t_{v}$

$t_{v} = -\frac{b}{2a} = -\frac{80}{2*(-4)} = 10$

The rabbit population will reach its peak after 10 years.