Question

John is organizing a local event. He expects the approximate attendance for the event to be modeled by the function a(t) = -16t2 + 48t + 64, where t is time in hours. Assuming the event ends when there are no attendees, plot the domain to represent the duration of the event. line plot

Answer 1

the duration of this event is 4 hours

Explanation:

This function is a quadratic one

let Δ be the dicriminant :

• a = -16
• b = 48
• c= 64
• Δ = 48²-4*(-16)*64 = 6400

so there are two values that satisfy -16t²+48t+64 = 0 x and y

• x= (-48+80)/-16*2 = -1
• y= (-48-80)/-16*2= 4

x<0 so w won't take it since time is a positive value here

so t = y = 4h