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 O an average maximum catch of ʼ salmon per day occurring in years ending with 5.t (Note: This exercise corresponds to the subsection Characteristics of a Sine Function and requires use of the formulas for average value, amplitude, period, and horizontal shift to construct sine models rather than curve-fitting using technology.) (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 rx) = a sin(bx + c) + d, where x = 0 corresponds to the year 1880. (Round your answers to three decimal places.)
(b) Calculate the amplitude and average value of the salmon catch cycle amplitude average value salmon per day salmon per day (c) Use the constants from parts (a) and (b) to construct a sine model for the average daily salmon catch. (Round all numerical values to three decimal places.)