Make some brief comments on how accurately the model found reflects the real world data. Is it accurate over the three days?

1. The water depth of a diurnal tide, y, measured in metres at the Swan River in Western Australia varies approximately sinusoidally in a daily cycle. In this task, you will use the WillyWeather website to construct a sinusoidal model for the rivers tide data over the three days spanning Thursday 14/03/2019 to Saturday 16/03/2019. (a) Find a formula y = f(t) = d + A sin [k (t )] which approximately models the water depth, where t is measured in hours after midnight at the beginning of the Thursday. To do this, use the tide data on the website and calculate the following (where you may round your calculations to 2 decimal places): (i) An approximation of the amplitude A. (ii) An approximation of the mean value d. (iii) An approximation for the period p. (iv) An approximation for the horizontal shift , by using y = f(t) = d + A sin [k (t )] with the values for A, d and p found above and the tide data of only Thursday 14/03/2019 (for reasons of calculator round-off errors). (b) Plot or sketch a large, neat and accurate graph of y = f(t) over the full three days, starting at t = 0. (c) Make some brief comments on how accurately the model found reflects the real world data. Is it accurate over the three days? What are some similarities or differences? Would this model work well for longer time periods?