Question 1
Paper 2, calculatorMedium7 marksAn employer models an employee’s salary at the start of each year using a geometric sequence. The salary at the start of year 1 was $40,000, and the salary at the start of year 5 was $48,620.25. Let denote the modelled salary, in dollars, at the start of year
(a)[2]
State the first term and determine the positive common ratio.
(b)[2]
Determine the modelled salary at the start of year 9, to the nearest cent.
(c)[2]
Hence write the total of the modelled salaries for the first nine years as a sum in sigma notation, and determine this total to the nearest cent.
(d)[1]
State one reason why this model may become unreliable when used to predict salaries many years into the future.