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Answer :
Amplitude 42,
Frequency 1/100 per hour,
Vertical Shift 55,
Phase Shift -4 hours.
AMPLITUDE: The amplitude (A) is half the difference between the maximum and minimum values. Therefore,
A = (97 - 13) / 2 = 42.
FREQUENCY: Frequency (f) is the reciprocal of the period (T). Given T = 100 hours,
f = 1 / T = 1 / 100 per hour.
VERT. SHIFT: The vertical shift (D) is the average of the maximum and minimum values. Therefore,
D = (97 + 13) / 2 = 55.
PHASE SHIFT: The phase shift (φ) is determined by where the maximum value occurs. A cosine function typically has its maximum at t = 0, but here it is at t = 4. Thus,
φ = -4 hours.
WORK: The cosine function can be written as:
y(t) = 42 cos(2π(1/100)(t + 4)) + 55
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