Use geometric sequences to model and analyse practical situations involving geometric growth and decay (use of logarithms not required), e.g. modelling the growth of a bacterial population that doubles in size each hour, calculating the value of an item using the diminishing-value method of depreciation.

A marine biologist is monitoring a coral reef. The reef's fish population at the start of 2023 was 8{,}400. Due to environmental changes, the population decreases by 6% each month. (a) Write a geometric sequence formula to model the fish population, where the first term represents the population at the start of 2023. (1 mark) (b) Calculate the expected fish population at the start of the fifth month (start of May 2023), correct to the nearest whole number. (2 marks)

A car is purchased for \$48,000. Each year, the car depreciates to 85% of its value from the previous year. Which option shows the car's value after four years?

A swimming pool chemical system uses an automatic top-up that adds water each day. Suppose the volume of water removed by evaporation each day is 8% of the current volume. The pool starts with a volume of 42,000 litres. (a) Write a geometric sequence formula for the volume remaining after \(n\) days. (b) Calculate the volume of water remaining in the pool after 6 days, correct to the nearest litre.

A scientist observed that the population of a bacterial culture is increasing by 25% each hour. At 9:00 am, there were 800 bacteria. (a) Write a geometric sequence to model the bacterial population at the end of each hour after 9:00 am. (1 mark) (b) Calculate the population at the end of the fourth hour (at 1:00 pm), rounding to the nearest whole number. (2 marks)