Question

the depth underwater,d, in meters, of Daisy the dolphin during a dive can be modelled by d=0.1t^2 - 3.5t +6, where t is the time in seconds after the dolphin begins her decent towards the water. how long was Daisy underwater ?

Answer 1

Setting d = 0 gives the points where she is at the surface.
therefore 0= 0.1t^2 - 3.5t + 6
apply the quadratic formula to get t = (3.5+- √12.25-4*0.1*6)/0.2
t = (3.5  3.1384709653)/0.2
t= 1.80764517352 and 33.1923548265
subtract the 2 to get the time difference between entry and exit you get
Δt = 31.384709653 seconds

That's as long as I haven't made a mistake :D