PATTERNS, FUR1 2014 VCAA 3 MC

A city has a population of 100 000 people in 2014.
Each year, the population of the city is expected to increase by 4%.
In 2018, the population is expected to be closest to

A. `108\ 000`

B. `112\ 000`

C. `115\ 000`

D. `117\ 000`

E. `122\ 000`

Show Answers Only

`D`

Show Worked Solution

`text(Population is a geometric sequence with)`

`a = 100\ 000,\ \ \ \ r = 1.04`

`P_1 (2014)`	`= a = text(100 000)`
`P_2 (2015)`	`= ar^1 = text(100 000) (1.04) = text(104 000)`
`vdots`
`P_5 (2018)`	`= ar^4 = text(100 000) (1.04)^4 = text(116 985.8…)`

`∴\ text(In 2018, the population will be closest)`

`text(to)\ 117\ 000.`

`=> D`