Question

The city of Townsville has a population of 2 million in 2002, which is growing at 6% per year.A) Write a recursive formula for the population of Townsville.B) Write an explicit formula for the population of Townsville.C) how many people will there be in 2011, rounding to the nearest tenth of a million?

Answer 1

Given:

Population in 2002 is 2 million and is growing at 6%per year.

A)

Recursive formula:

`P_n=P_(n-1)(1+(6)/(100))`
`P_n=P_(n-1)((100+6)/(100))`
`P_n=P_(n-1)((53)/(50))`
`P_0=2.2`
`\text{ }`
`P_n=P_(n-1)(1.06)`

B)

`P_1=P_0(1.06)`
`P_2=P_1(1.06)`
`P_2=P_0(1.06)_{}(1.06)`
`P_2=2.2(1.06)^2_{}`
`P_n=2.2(1.06)^n_{}`

C)

n=2011-2002

n=9

`No\text{ of people in 2011=}2.2(1.06)^9`
`No\text{ of people in 2011=}3.7\text{ millon}`