# Sequences and Series

• Apr 18th 2010, 12:50 PM
bhuang
Sequences and Series
The question is posted below and I have attached my solution, which is close to the values in the answer section, but only when I round it.

Each year for the past five years the population of a certain counry has increased at a steady rate of 2.7% per annum. The present population is 15.2 million.
a) What was the population one year ago?
b) What was the population five years ago?

My solution:
U6 (6th term)=15.2 million
common ratio=1.027
U1 = first term

U6 = U1(1.027)^5
15.2 million = U1(1.027)^5

Therefore, b) U1=13.3 million
and a) U5 (fifth term) = U1(1.027)^4
= 13.3(1.027)^4
= 14.8 million

Now, the answer in the book is: a) 14 793 187 b) 13 271 941
even if I don't round my values, they still aren't the same as the book's. Did I do this question right?
• Apr 18th 2010, 12:59 PM
AllanCuz
Quote:

Originally Posted by bhuang
The question is posted below and I have attached my solution, which is close to the values in the answer section, but only when I round it.

Each year for the past five years the population of a certain counry has increased at a steady rate of 2.7% per annum. The present population is 15.2 million.
a) What was the population one year ago?
b) What was the population five years ago?

My solution:
U6 (6th term)=15.2 million
common ratio=1.027
U1 = first term

U6 = U1(1.027)^5
15.2 million = U1(1.027)^5

Therefore, b) U1=13.3 million
and a) U5 (fifth term) = U1(1.027)^4
= 13.3(1.027)^4
= 14.8 million

Now, the answer in the book is: a) 14 793 187 b) 13 271 941
even if I don't round my values, they still aren't the same as the book's. Did I do this question right?

This type of question is modeled by

\$\displaystyle P=Pie^{rt}\$

Where r = rate, t = time, Pi= Initial Population. Let us define t in years. Let us find the intial Population

\$\displaystyle 15.2 = Pie^{.027(5)}\$

\$\displaystyle Pi=13.28\$

Now let us find the population at year 4

\$\displaystyle P=13.28e^{(.027)(4)}=14.8\$

Your book asks for the answers in reverse order. Oh and this is not a sequence or series question, it is an exponential growth question (for future reference)! You got the same answers as me, yes your answers are correct.