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+\frac{6}{100})$$P_n=P_{n-1}(\frac{100+6}{100})$$P_n=P_{n-1}(\frac{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}$