Question

at time t, in hours, a lake is covered with ice of thickness y cm, where y = .5 t^1.5 . if ice forms for 0 <= t <= 6, at what time in this interval is the ice thickest? at what time is the ice forming fastest?

Answer 1

Y = .5 * t^(1.5)
Points on the graph are:
( 0, 0 ) , ( 1 , .5 ), ( 2 1.41 ), ( 3, 2.5985 ), ( 4 , 4 ), ( 5 , 5.59 ) , ( 6, 7.34 ).
Answer:
The ice is thickest at t = 6.
The ice is forming fastest at t = 6.