Question

1. Wintertime temperatures in a small town in the Sierra Nevada Mountains range from a minimum of 19°F to a maximum of 39°F, with the minimum temperature occurring at 2 a.m. in the morning. a. Find a sinusoidal model for the wintertime temperatures in this town. That is, find a function formula for the temperature in this town, y = f(t), where t is the number of hours since midnight b. Use your model to estimate the temperature at 4 p.m. Use your model to find the time of the day when the temperature is 35°F. c.

Answer 1

Date Page Sinusoidal Function is of the form y = A SIN B(x-C) +D Maximum 11 a) Given that Minimum Temperature = 19°f at t=2 = 39 period. Amplitude A= (Max) A= (Max) – (Min. Temp) – 39-19-20-10. - 24 hours 2 2 - 21 B = 1 12 A=101, B =21 period 2 Vertical shift D = Max + Min = 39+19=58-29 2 It will take 6 hours to reach t=6 bhours average temperature from minimum temperature 24 Average temperature of 29°F at t=2+6=8hous C= 8 hours. ni y=f(t) = losino (+8)+291 12 123 D At4pm ,t=16, f(16) = 10 sina = 10 sinu 8 +29 f(16) = lo sin 211 +29 - 37.66€ Temperature at 4pm is 37.66 For 38r To find t, when f(t) = 35°F frounded bo nearest 35= 10 SNI (+-8) +29 25 - 24 =le sing (4-8) > $val (a - b) x 2 +8=t > t=1.458, 17,542 t=10.46 am 15. 54 pm c) Whole number 12 to