The table below provides the monthly high temperature in Calgary, Alberta for 2021

Month Temperature C

1 January 9.7

2 February 9.4

3 March 18.7

4 April 21.7

5 May 27.2

6 June 36.3

7 July 36.3

8 August 34.2

9 September 27.4

10 October 23.7

11 November 17.2

12 December 13.3

a) Find the equation of a sinusoidal regression function y = asin(bx + c) + d that best models the

data. Express the values of a, b, c, and d to the nearest tenth. (1 mark)

b) Interpret the values of a and d in the above regression equation with respect to Calgary's monthly

high temperature. (2 marks)

c) Algebraically determine, using your equation from part a, the predicted daily high temperature in

Calgary in December 2022 to the nearest tenth. (1 mark)

d) Sketch the graph of this regression equation below for 2021 and 2022. Be sure to label each axis

and the scale used on each axis. (2 marks)

e) Indicate on your sketch the point where the monthly high temperature will reach 25C for the

second time in 2022. Include the coordinates of this point rounded to the nearest whole number.

What month is represented by this point? (1 mark)