General Mathematics · Unit 3 · Time series analysis · Analysing time series data
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A council records the annual rainfall (mm) at a monitoring station over four consecutive years: Year 2021: $850$ mm Year 2022: $920$ mm Year 2023: $1{,}010$ mm Year 2024: $1{,}080$ mm Assuming a linear trend, calculate the predicted annual rainfall for 2027, correct to the nearest 10 mm.
A municipal council tracks the number of visitors to its community sports centre at the end of each quarter. The data for the four quarters of 2024 are shown in the table below. (a) Determine a linear model for the number of visitors, where $x$ represents the number of quarters after the end of Q4 2024. (1 mark) (b) Using your model, predict the number of visitors at the end of Q2 2025. (1 mark) (c) Comment on the reliability of your prediction. (1 mark)
A regional council monitors the monthly water consumption (kilolitres) of a growing suburb over a four-year period to plan future infrastructure needs. The data is recorded at the end of each year from 2022 to 2025. Using the data provided: (a) Determine a linear model for the suburb's water consumption, where \(x\) represents the number of years after the end of 2022 and \(y\) represents the monthly water consumption in kilolitres. (b) Use your model to predict the monthly water consumption at the end of 2028. (c) The council plans to upgrade the water supply system if monthly consumption exceeds 8,500 kilolitres. Determine whether the upgrade will be needed by the end of 2028 based on your prediction.