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 is the day of the year.
Hours of Daylight on the Middle Day of Each Month
Month Day of the Year Ottawa, ON (45° N Lat.) Regina, SK (50° N Lat.) Whitehorse, YT (60° N Lat.)
January 15 8.9 8.5 6.6
February 45 10.1 10.1 9.2
March 75 11.6 11.8 11.7
April 106 13.3 13.7 14.5
May 136 14.7 17.1 22.2
June 167 15.4 16.4 18.8
July 197 15.1 15.6 17.5
August 228 13.8 14.6 15.8
September 259 12.2. 12.7 13.8
October 289 10.7 10.8 10.2
November 320 9.3 9.1 7.6
December 350 8.6 8.1 5.9
A. Use the data in the table to estimate when carnations will start to bloom in Ottawa, Regina, and Whitehorse.
B. Plot the data for Regina on a scatter plot, and draw a curve of best fit. Use your graph to determine the amplitude, period, and equation of the horizontal axis.
C. Use your estimate in part A to create an algebraic model for the Regina data. Use sinusoidal regression on a graphing calculator to check your results.
