Salmon Fishing (Historic) A fishing club on the Restigouche River in Canada kept detailed records on the numbers of fish caught by its members between 1880 and 1930. Average catch tends to be cyclic each decade with the average minimum catch of 0.9 salmon per day occurring in years ending with 0 and average maximum catch of 1.7 salmon per day occurring in years ending with 5.
(Source: E. R. Dewey and E. F. Dakin, Cycles: The Science of Prediction. New York: Holt, 1947)
a. Calculate the period and horizontal shift of the salmon catch cycle. Use these values to calculate the parameters b and c for a model of the form f (x) = a sin (bx + c) + d.
b. Calculate the amplitude and average value of the salmon catch cycle.
c. Use the constants from parts a and b to construct a sine model for the average daily salmon catch.
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