Display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations.

A wildlife park releases a population of endangered birds. The population at the end of each year follows a geometric sequence with first term \(a = 120\) birds and common ratio \(r = 1.25\). (a) Complete the table showing the population for Years 0 through 4. Round all values to the nearest whole number. (1 mark) (b) Display this data in a scatterplot with labelled axes, using Year as the independent variable. (2 marks)

A colony of bacteria triples every hour. The initial population at hour 0 is 200 bacteria. A table showing the first three hours is provided. Determine the population of bacteria at hour 4.

The resale value of a motorcycle shows geometric decay. Determine the resale value four years after purchase.

A mobile phone depreciates by 15% each year. Its initial value is $1,200. (a) Complete the table showing the phone's value at the end of each year for the first four years. (1 mark) (b) Display this data on a scatterplot with labelled axes, plotting the phone's value against the year number. (2 marks)