The tide depth in Deep Cove, British Columbia, from 4:00 to 15:00 on January 6
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The tide depth in Deep Cove, British Columbia, from 4:00 to 15:00 on January 6

2. The tide depth in Deep Cove, British Columbia, from 4:00 to 15:00 on January 6, 2011, can be modelled accurately by the polynomial function:

f(t) = 0. 001t 3 − 0. 055t 2 + 0. 845t + 0. 293

 where f(t) is the tide depth in metres and t is the number of hours after midnight.

a) What is the tide depth at 14:00 on January 6 (to the nearest tenth of a metre)?

b) When is the tide depth the greatest on January 6?

c) What are the restrictions on the variable t? Does this match the domain of the function?

d) How would you use this data to determine the tide depth on January 7, 2011?

Hint
Mathematics"b) The typical tidal range in the open ocean is about 0.6 metres (2 feet) (blue and green on the map on the right). Closer to the coast, this range is much greater. Coastal tidal ranges vary globally and can differ anywhere from near zero to over 16 m (52 ft). The Four Different Types of Tides: a. Diurnal Tide. A diurnal tide has one episode of high water and one episode of low wa...
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