The Bay of Fundy in North America has some of the largest va

The Bay of Fundy in North America has some of the largest varying tidal depths on the planet. e ep of the water there is at lowtide at 11:00AM and high tide is at 6:00PM, and lowtide is 3m depth and high tide is 17m. Use a sine model to answer the following questions. how deep is the tide at 1:00AM? How fast is the tide changing, and in what direction, at 8:00PM?

Solution

HEre the required model will be represented by the sine function o f form

y=Asin Bx

Here amplitude A =17-3= 14

and its half period pi/B = 18-11=7

so B= 3.14/7 = 0.4486

so required function is y=14sin (0.4486x)

Now when for 1:00 A.M. x= 2, so

y= 14 sin (0.4486 x 2) = 14 sin(0.8971) =14 x 0.7815 = 10.94

So at 1:00 pm, it is 10.94 ft deep.

Answer of part a)

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Now for second part, we differentiate above function with respect to x as :

dy/dx = 14cos (0.4486x)(d/dx)(0.4486x) = 14(0.4486) cos (0.4486x) =6.2804 cos (0.4486x)

Now as 8 p.m. , x= 9

so at this point dy/dx = 6.2804 cos (0.4486(9)) = 6.2804cos(4.0374) = 6.2804 x (-0.6249) = -3.92

that means (-) signn shows that its direction is downwards towards lowtide and its seed is 3.92 m per hour.

Answer