Need help on setting up an equation of population

[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 = X₀e^rt
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!

 

[fzero]

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.