• Nov 27th 2008, 02:06 PM
bhuvan
Assume that the population of the world in 2002 was 6.2 billion and is growing at the rate of 1.3% a years.
(a) Set up a recurrence relation for the population of the world n years after 2002.

(b) Find an explicit formula for the population of the world n years after 2002.

(c) what will the population of the world be in 2022?
• Nov 27th 2008, 03:03 PM
Soroban
Hello, bhuvan!

Quote:

Assume that the population of the world in 2002 was 6.2 billion
and is growing at the rate of 1.3% a years.

(a) Set up a recurrence relation for the population of the world $\displaystyle n$ years after 2002.

$\displaystyle P_o \:=\:6.2$
billion

$\displaystyle P_n \;=\;1.013\!\cdot\!P_{n-1}$

Quote:

(b) Find an explicit formula for the population of the world n years after 2002.

$\displaystyle P(n) \;=\;6.2(1.013)^n$
billion

Quote:

(c) What will the population of the world be in 2022?

When $\displaystyle t = 20\!:\;\;P(20) \;=\;6.2(1.013)^{20} \;\approx\;8.0275$
billion
.
• Nov 28th 2008, 08:16 AM
bhuvan
Thank You !!