Hungry Harry is a giant ogre with an even bigger appetite. After Harry wakes up from hibernation, his daily hunger H(t) (in kg of pigs) as a function of time t (in hours) can be modeled by a sinusoidal expression of the form a*cos(b*t)+d. When Harry wakes up at t=0, his hunger is at a maximum, and he desires 30kg of pigs. Within 2 hours, his hunger subsides to its minimum, when he only desires 15kg of pigs. Find H(t). t should be in radians. H(t)=

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Hungry Harry is a giant ogre with an even bigger appetite. After Harry wakes up from hibernation, his daily hunger  H(t) (in  kg of pigs) as a function of time  t (in hours) can be modeled by a sinusoidal expression of the form  a*cos(b*t)+d. When Harry wakes up at  t=0, his hunger is at a maximum, and he desires  30kg of pigs. Within 2 hours, his hunger subsides to its minimum, when he only desires  15kg of pigs. Find  H(t).  t should be in radians.  H(t)=

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Calculate Average Hunger Level: Harry's maximum hunger is 30kg at t=0, so d + a = 30. Since the cosine function starts at its maximum, d is the average of the maximum and minimum hunger levels.Find Amplitude: Calculate the average hunger level to find d. (30kg + 15kg) / 2 = 22.5kg So, d = 22.5kg.Determine Full Period: The amplitude a is half the difference between the maximum and minimum hunger levels. a = (30kg - 15kg) / 2 = 7.5kgConvert Period to Radians: Harry's hunger reaches its minimum in 2 hours, which is half the period of the cosine function. Therefore, the full period is 4 hours.Solve for b: Convert the period from hours to radians since 1 hour = π/12 radians. Period in radians = 4 hours * (π/12 radians/hour) = π/3 radiansThe period T of a cosine function is related to b by T = 2π/b. Solve for b using the period in radians. π/3 = 2π/b b = 6

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