Final answer:
To model the daylight hours, we use a sinusoidal function with an amplitude of 3.7 hours, a midline of 12 hours, and a horizontal shift to accommodate the longest day on June 21. Plugging in the values for April 3, we estimate roughly 9.2 hours of daylight.
Step-by-step explanation:
To model the number of hours of daylight in Lethbridge, Alberta, we use a sinusoidal function because daylight length fluctuates in a predictable, wave-like pattern over time. Given that the longest day occurs on June 21 (summer solstice) with 15.7 hours of daylight and the shortest day on December 21 (winter solstice) with 8.3 hours of daylight, we can denote these dates as the extremes of our sinusoidal function. The sinusoidal function has a period of one year, or 365 days, and a midline that represents the average hours of daylight, which is halfway between the longest and shortest daylight lengths.
To find the specific model, we need to determine the amplitude, midline, and horizontal shift. The amplitude is half the difference between the longest and shortest day lengths: (15.7 - 8.3) / 2 = 3.7 hours. The midline is the average of these day lengths: (15.7 + 8.3) / 2 = 12 hours. Since the maximum occurs at June 21, which is approximately 172 days into the year, our horizontal shift will account for this. A rough estimate of the sinusoidal model would be:
L(t) = 12 + 3.7sin[(2π/365)(t - 172)]
Now, to find the number of hours of daylight on April 3, we calculate:
L(93) = 12 + 3.7sin[(2π/365)(93 - 172)] = 12 + 3.7sin(-1.54) ≈ 12 - 2.8 ≈ 9.2 hours
Thus, on April 3, there would be approximately 9.2 hours of daylight in Lethbridge, Alberta.