SOLUTION: The number of people who are sick t days after the outbreak of a flu epidemic is given byn the equation p=-t^(2)+100t+25. What is the maximum number of people sick during the outbr

 

Hi,

p=-t^(2)+100t+25 where t the number of days after the outbreak

What is the maximum number of people sick during the outbreak?

Using the vertex form of a parabola,  where(h,k) is the vertex

p=-t^(2)+100t+25

p=-(t^(2)-100t)+25

p=-[(t-50)^2 - 2500] + 25

p = -(t-50)^2 + 2525  Vertex is Pt(50,2525)

|Parabola opening downward : a = -1 < 0

 2525 is the maximum number of people sick during the outbreak 

(which occurs 50 days after the outbreak)