# Need help on setting up an equation of population

• Vintageflow
In summary, The student is struggling with a homework assignment on population growth and is given several variables to use, including the original population (J), generation (Y), new population after each generation (P), born percentage (b), and death percentage (d). The student is attempting to use an exponential function, but it does not give the desired answer. Instead, the student attempts a different solution, but it is still not correct. The correct formula for discrete growth is P(Y) = (1 + (b-d))Y J. It is possible that any discrepancies in the results may be due to rounding errors in a computer code.
Vintageflow
1. So for my computer science course I was given the homework on how to write a program on population growth. The serious dilemma is how to set up the equation. Here are the variables that are given to me:

J = original number of Jackalopes (the imaginary animal that my teacher used)
Y = generation (no specific unit of time)
P = new population after each generation
b = born percentage each generation (3% or 0.03)
d = death percentage each generation (1% or 0.01)

Example: J = 40 Jackalopes
Y = 100 generations
P = new population of 291 Jackalopes after 100 generations

2. The most relevant equation is population growth, which involves exponential functions. the equation looks like

X = X0ert
where:
X0 is the original population
r is the net rate of growth
t is time

The big problem is I can't use exponential functions, because I need to truncate the results and using exponential functions don't give the answer that my teacher is looking for.

3. Here is the attempted solution I came up with:

P = J + (J(0.03-0.01))Y

unfortunately my answer is way off. I recognize the pattern when I attempted to do the equation, but I don't know how to set it up. Please help me!

Vintageflow said:
3. Here is the attempted solution I came up with:

P = J + (J(0.03-0.01))Y

After one generation,

P(1) = J + (b-d)J = (1+(b-d)) J

After Y generations,

P(Y) = (1 +(b-d))Y J.

It's possible to derive an exponential law if we treat a continuous growth, but this formula is fine for discrete growth. If find P(100)=290, the discrepancy might be due to round off error in a computer code.

## 1. How do I determine the initial population for an equation?

The initial population can be determined by looking at the population at a specific time, usually denoted as t=0. This can be found in historical data or by making an educated estimate based on the population growth rate.

## 2. What is the formula for calculating population growth rate?

The formula for calculating population growth rate is (birth rate - death rate) + (immigration rate - emigration rate). This takes into account both natural population growth and migration to estimate the overall population growth rate.

## 3. How do I incorporate a carrying capacity into the population equation?

A carrying capacity can be incorporated into the population equation by using the logistic growth model, which takes into account the maximum population that an environment can sustain. This is represented by the letter K in the equation.

## 4. What is the difference between an exponential growth model and a logistic growth model?

An exponential growth model assumes unlimited resources and an unbounded environment, resulting in a continuously increasing population. A logistic growth model takes into account a carrying capacity and results in a population that reaches a stable equilibrium over time.

## 5. Can I use the population equation to predict future population growth?

Yes, the population equation can be used to make predictions about future population growth. However, it is important to note that these predictions are based on assumptions and may not accurately reflect real-world population changes.

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