# The Tide in Bay of Fundy: The Depths of High and Low Tides

Date of Exam:

**Problem**

The tide in Bay of Fundy rises and falls every 13 hours. The depth of the water at a certain point in the bay is modeled by a function *d* = 5 sin (2π/13)*t* + 9, where *t* is time in hours and *d* is depth in meters. Find the depth at *t* = 13/4 (high tide) and *t* = 39/4 (low tide).

- The depth of the high tide is 15 meters and the depth of the low tide is 3 meters.
- The depth of the high tide is 16 meters and the depth of the low tide is 2 meters.
- The depth of the high tide is 14 meters and the depth of the low tide is 4 meters.
- The depth of the high tide is 17 meters and the depth of the low tide is 1 meter.

**Answer Key**

[ C ]

**Solution**

$d = 5 \sin \left( \dfrac{2\pi}{13} \right)t + 9$

$d = 5 \sin \left[ \left( \dfrac{2\pi}{13} \right) \cdot \dfrac{13}{4} \right] + 9$
$d = 5 \sin \left[ \left( \dfrac{2\pi}{13} \right) \cdot \dfrac{39}{4} \right] + 9$

When *t* = 13/4

$d = 5 \sin \left( \dfrac{\pi}{2} \right) + 9$

$d = 14 ~ \text{m}$

When *t* = 39/4

$d = 5 \sin \left( \dfrac{3\pi}{2} \right) + 9$

$d = 4 ~ \text{m}$

The depth of the high tide is 14 meters and the depth of the low tide is 4 meters.

Answer = [ C ]

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