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MTH 112 FWH 6 – Modeling with Trigonometric Functions
1. The outside temperature over the course of a day can be modeled as a sinusoidal function.
Suppose you know the temperature varies sinusoidally between 52 and 76 degrees throughout
the 24 hour day with the average temperature occurring at midnight. Determine a function
modeling the temperature throughout the day and then determine which hours of the day the
temperature is above 70 degrees.
2. Suppose the high tide in Seattle occurs at 1:00 am and again at 1:00 pm at which times the
water is 10 feet above the height of low tide. Low tide occurs 6 hours after the high tides.
Supposing there are two high tides and two low tides every day and the height of the tide
varies sinusoidally, find a formula for the function y = h(t) that computes the height of the
tide above low tide at time t. (So y=0 corresponds to low tide). Then determine the tide
height at 11:30am. Finally, determine the hours of the day when the tide is less than or equal
to 3 feet above low tide.
3. Find a function of the form y = a sin
x + m + bx that fits the data:
4. Find a function of the form y = abx cos
x + c that fits the data:
5. A spring is attached to the ceiling and pulled 19 cm down from equilibrium and released.
After 4 seconds the amplitude has decreased to 14 cm. The spring oscillates 13 times each
second. Assuming exponential amplitude decay, determine a function which models the
distance, D, the end of the spring is below equilibrium in terms of seconds, t, since the spring
was released. Hint: To find the factor of exponential decay, note that the initial amplitude is
19 and then look at A(t) = A0 · bt is the amplitude function and plug in (4,14) into this to
solve for b.
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