Question

1. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature for the day is 82 degrees and the low temperature of 68 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

D(t)=

2. A population of rabbits oscillates 18 above and below an average of 62 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t.
P(t) =   

What if the lowest value of the rabbit population occurred in April instead?
P(t) =   

3. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 65 degrees occurs at 4 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 6 AM.

degrees :

4. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 62 and 88 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after midnight, to two decimal places, does the temperature first reach 72 degrees?

hours:

5. A Ferris wheel is 20 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. How many minutes of the ride is spent higher than 20 meters above the ground?

minutes:

Answer 1

given that 82 high temperature low temperature 7 68 Amplitude 82 - 68 14 2 2 Lel- BLt) - Asin ( Bt + c) to high temperaturet low tempe -rature CH 82 +68 2 1.50 75 period 2.4 hour ZT 24 - DLE) = Since 75 + 7 sin LA t + c) alt=3, D(t)= 68 68-75 + 7 sin (7 * 3+C) (11 (3) tc ) in (A + c) = -tsit I) 7- 7 sin sin - 7 - I - = -3 -3T q

y = 7 sintet - 37 ) +75 y = 7 sin ( 17 ore (t- g) + 75 since poolouration oscillates by above below, A-18 Average 62 ardd to o lowest valen 62-18 - 46 PLE) - A sin ( Bt + c) to PL A = 18 D ²62 T B - 21 1 - PLEJ = 18[sin (fite)) +62

46 too PLE- - 46 = 18 sin ( 7 Log+c) toe -18-18 sin (xotc) Sink) = -) i c = -t Plt) - 18 sin gt-k toe PLE) = 18 sin ( 7 (E-3)) + 62 of lowest value of the rabbilt occurs in Alonie then at t=4, Plt - 46 polowlation 196 -18-18 Sin 18 sinf 7x4 + c) +62 15+) - 7 H A - 2x _ _37 28 tc 3 - -37-4T

-75 1. PLZ) = 18 sin (Alt-7)+62 high temperature 265 degree low temperature = 65-60-5 degree average temperature = 60 degree period - 65-60 24 hours ET TA 2 A = 5 Led- Olt - Asin ( Bt+c) + 1 De average tempo A&Amphetande it at time 4PM, DLE)- 65 and ta 16 65= 4.5) Sin Late ( t) +cJ+60 5=esssin (A x 16 + c) sin ( 4* 4 T + C) = 1 štte 플

X 45 23 5. 6 ..DLE) = 5 sin (Tet -SA) +60 Sin 2 - 1)) 6 25 sin t bo Diameter of Ferris Wheel rometer A-90 Platefem from aground is 4m 4+10= 1am. period 4 minute - B - 27 besied - 27 - A

91- hlt - 4 td- 600 position is reference, then to, y - hlt) Asin (Bt + c) to ht) - 10 sin (27 t + c) + 14 at tzo, hlt - 4 to sin. It toe) +14 -10th lo sin Latte) Atte - I tot 4 z I kld A