Name: Gina

Who is asking: Student
Level: Secondary

Question: Hello. I am stuck on the following question:

Suppose the population of a country increases at a steady rate of 3% a year. If the population is 50 million at a certain time, what will it be 25 years later? Define the recurrence relation that solves this problem.

I'm not even sure how to start off this problem and I am having trouble figuring out the recursive function for this problem. I would very much appreciate it if you could help me! Thank you!!

Hi Gina, If the population was 50 million in some year then it will be 50 million plus 3% more in a year. That is at the end of year 1 the population will be

50 million + 3/100 x 50 million
= (1.03) x 50 million

At the end of the second year the population will be (1.03) x 50 million plus 3% of (1.03) x 50 million, that is

[(1.03) x 50 million] + 3/100 x [(1.03) x 50 million]
=[(1.03) x 50 million] x (1.03)
= (1.03)2 x 50 million

What will the population be at the end of the third year?
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