What is the Geometric Progression for Rabbit Population Growth?

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Homework Help Overview

The problem involves determining the growth of a rabbit population over several years, starting with an initial number of rabbits represented by b. The relationship between the population at the beginning and end of the first year is given, leading to questions about the nature of the progression (arithmetic or geometric) and how to express the population at subsequent years.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss whether the population growth can be modeled as an arithmetic progression (AP) or a geometric progression (GP), with some suggesting that it may not fit either model. There are attempts to derive expressions for the population at the second and third years based on the initial conditions.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have provided expressions for the populations at the second and third years, while others suggest looking for patterns in the sums of populations over the years. No consensus has been reached on the nature of the progression.

Contextual Notes

There is uncertainty regarding whether the population growth should be classified as an AP or GP, and participants are encouraged to generalize the relationship based on the information provided. The original problem does not specify the type of progression, leading to varied interpretations.

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Homework Statement



Number of rabbits reared by Alice at the beginning of certain year is given as b. End of that particular year, the number of rabbits were given as 10+(3/2) b . Write down the number of rabbits at the end of second and third year. Find the total number of rabbits at the end of nth year.

Homework Equations





The Attempt at a Solution



It doesn't tell whether the increase in the number of rabbits is an AP or GP but it could have been a GP according to the next part of the question. Assuming that its a GP,

common ratio, r= (20+3b)/(2b)

Then, T2 = (10+3/2 b)((20+3b)/(2b))

??
 
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thereddevils said:
It doesn't tell whether the increase in the number of rabbits is an AP or GP but it could have been a GP according to the next part of the question.
While a geometric progression certainly makes more sense than an arithmetic progression here, what makes you think those are the only two options? All you have been told here is the relation between the population at the start and end of year 1. So, generalize this. Assume that the population at the end of some year is 10 + 3/2 times the population at the start of that year. Note that the population at the start of some year is the same as the population at the end of the previous year.
 


Just to further this point - it really is neither - if you write down a few terms, you will clearly see that it is neither arithmetic or geometric, so what you know about these two types of series goes out the window.
 


ok thanks. I got T2=25+(3/2)^2 b and T3=95/2+(3/2)^3 b. How do i find the total population at the nth year?
 


Why don't you start by writing the the sums for the first, second, and third years, and maybe see a pattern?
 

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