Answered

17. The hourly temperature at Portland, Oregon, on a particular day is recorded below.

1 A.M. 2 3 4 5 6 7 8 9 10 11 12 Noon
46° 44° 43° 41° 40° 40° 41° 43° 46° 52° 65° 69°
1 P.M. 2 3 4 5 6 7 8 9 10 11 12 Midnight
72° 74° 75° 75° 77° 75° 74° 70° 62° 55° 51° 48°

a. Find the amplitude of a sinusoidal function that models this temperature variation.
b. Find the vertical shift of a sinusoidal function that models this temperature variation.
c. What is the period of a sinusoidal function that models this temperature variation?
d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation.
e. What is the model’s temperature at 10 A.M.? Compare this to the actual value?

Answer :

Answer:

a. Amplitude: 19.65446

b. Vertical Shift: 58.00713

c. Period: 2/0.22797 = 27.56146

d. 19.65446 * sin(0.22797x + 1.79552) + 58.00713

e. Model's Temperature at 10 A.M.: f(-7) = 61.91

   This value is 9.91 degrees higher than the actual value.

Step-by-step explanation:

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