For this assignment, we will explore the use of technology to model a periodic function and its limits. The data you are using is from the following webpage from Fisheries and Oceans Canada:

Sandy Cove - Tides, Currents, and Water Levels

Instructions:

Step 1: Go to the Google Sheet shared by your teacher to access the tide data of Sandy Cove, Nova Scotia, for the first 13 days of February.

Step 2: We are going to plot water level (metres) versus time (hours). Copy and paste these two columns onto DESMOS. You do not need to type the data onto DESMOS yourself.

Step 3: Generate a sinusoidal model for the data. What do you notice?

Step 4: On DESMOS, make a new table of values for the first 12 days of February and generate a sinusoidal model for the data. What do you notice?

Step 5: On DESMOS, make a new table of values for the first 11 days of February and generate a sinusoidal model for the data. What do you notice?

Step 6: Keep decreasing the amount of data used to create the sinusoidal model. When do you see a model that has a R2 value that is greater than 0.9? Does this model seem to work for the first 13 days of February? Justify your choice.

Step 7: Lets try to find a model that describes the first 13 days of February by hand. Using what we have learnt in class, what is the equation of your model?

Step 8: Lets say we want to find out when the water level is 3.7 m on Day 0, within a 24-hour period.

a) Use your model from Step 6 to estimate the time in hour and minutes. (Read from the graph.)

b) Use your model from Step 7 to calculate the time by hand. (Not reading from the graph.)

c) Are your answers the same? If not, why do you think they are different?

Step 9: If we were to plot every single day of the month, what would happen to the equation of the resulting model? Will using more points increase the accuracy of the model?

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