2. Use sinusoidal regression (in radian measure) to create an algebraic model for Ottawa, Regina, and Whitehorse.  State the amplitude, period, and equation of the axis of the curve for each city.3. Use the algebraic model for each city to calculate:
a) when the hours of daylight first exceed 12 hours.
b) the interval in the year when there are more than 12 hours of daylight.
4. Compare the blooming season for carnations in the three cities.

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The flowering of many commercially grown plants in greenhouses depends on the duration of natural darkness and daylight. Short-day plants, such as chrysanthemums, need 12 or more hours of darkness before they will start to bloom. Long-day plants, such as carnations, need more than 12 h of daylight. The number of hours of daylight, h(t), varies with the latitude and the time of the year, t, where r is the day of the year. Month January February March April May June July August September October November December Day of the Year 15 45 75 106 136 167 197 228 259 289 320 350 Hours of Daylight on the Middle Day of Each Month Ottawa, ON (45° N Lat.) 8.9 10.1 11.6 13.3 14.7 15.4 15.1 13.8 12.2 10.7 9.3 8.6 Regina, SK (50° N Lat.) 8.5 10.1 11.8 13.7 17.1 16.4 15.6 14.6 12.7 10.8 9.1 8.1 Whitehorse, YT (60° N Lat.) 6.6 9.2 11.7 14.5 22.2 18.8 17.5 15.8 13.8 10.2 7.6 5.9 The flowering of many commercially grown plants in greenhouses depends on the duration of natural darkness and daylight. Short-day plants, such as chrysanthemums, need 12 or more hours of darkness before they will start to bloom. Long-day plants, such as carnations, need more than 12 h of daylight. The number of hours of daylight, h(t), varies with the latitude and the time of the year, t, where r is the day of the year. Month January February March April May June July August September October November December Day of the Year 15 45 75 106 136 167 197 228 259 289 320 350 Hours of Daylight on the Middle Day of Each Month Ottawa, ON (45° N Lat.) 8.9 10.1 11.6 13.3 14.7 15.4 15.1 13.8 12.2 10.7 9.3 8.6 Regina, SK (50° N Lat.) 8.5 10.1 11.8 13.7 17.1 16.4 15.6 14.6 12.7 10.8 9.1 8.1 Whitehorse, YT (60° N Lat.) 6.6 9.2 11.7 14.5 22.2 18.8 17.5 15.8 13.8 10.2 7.6 5.9

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To estimate when carnations will start to bloom in Ottawa Regina and Whitehorse based on the hours of daylight we can analyze the data given in the ta... View the full answer