1. Geometric progression

Hi, I have some questions on geometric series.

Estimates are produced for the number of babies born worldwide each year. The estimates for 2004 and for 2008, given in thousands of births to the nearest thousand, were 130350 and 137804 respectively. Assume that successive yearly estimates are in geometric progression.
a) Find the annual percentage increase in the number of births.
b) Find the estimates for 2006 and 2011 (to the nearest thousands)

I worked out a) correctly, the answer being 1.4%, but I'm not sure that my method was completely reliable, so I'd really appreciate it if someone could me the proper method. Also, the answers for b) are 134000, and 144000.

Any help would be greatly appreciated

2. Originally Posted by sakuraxkisu
Hi, I have some questions on geometric series.

Estimates are produced for the number of babies born worldwide each year. The estimates for 2004 and for 2008, given in thousands of births to the nearest thousand, were 130350 and 137804 respectively. Assume that successive yearly estimates are in geometric progression.
a) Find the annual percentage increase in the number of births.
b) Find the estimates for 2006 and 2011 (to the nearest thousands)

I worked out a) correctly, the answer being 1.4%, but I'm not sure that my method was completely reliable, so I'd really appreciate it if someone could me the proper method. Also, the answers for b) are 134000, and 144000.

Any help would be greatly appreciated
Please post what you have done.

CB

3. For a), this is what I did:

(137804 - 130350)/130350
= 7454/130350
(7454/130350) x 100
=5.718
5.718/4
=1.429
=1.4%

This method worked for this question, but it didn't work for another question I tried. This is the other question for which my method above didn't work for:
The profit made by a supermarket chain in 2004 is £700 million. The managing director wishes to increase this by 2% per year for the next 10 years. In fact, the profit increases annually in geometric progression to £765 million in 2009.
a) Find the annual percentage increase in profit from 2004 to 2009, giving the answer correct to 2.s.f.

For this question, the correct answer is 1.8%, but I got 1.9%, hence why I think my method above isn't very reliable, and why I would like it if someone could give me the proper method

4. Originally Posted by sakuraxkisu
For a), this is what I did:

(137804 - 130350)/130350
= 7454/130350
(7454/130350) x 100
=5.718
5.718/4
=1.429
=1.4%

This method worked for this question, but it didn't work for another question I tried. This is the other question for which my method above didn't work for:
The profit made by a supermarket chain in 2004 is £700 million. The managing director wishes to increase this by 2% per year for the next 10 years. In fact, the profit increases annually in geometric progression to £765 million in 2009.
a) Find the annual percentage increase in profit from 2004 to 2009, giving the answer correct to 2.s.f.

For this question, the correct answer is 1.8%, but I got 1.9%, hence why I think my method above isn't very reliable, and why I would like it if someone could give me the proper method
If the annual percentage increase is $\displaystyle $$r, then the number of births: \displaystyle N_{2008}=(1+\frac{r}{100})^4 N_{2004} and you need to solve for \displaystyle$$r$

CB