What is the population total at one hundred years if you begin with two animals and they reproduce at 25% annually?
To determine the population total after 100 years, starting with two animals and assuming they reproduce at a rate of 25% annually, we can use the formula for compound interest.
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the final amount (population total)
P = the initial amount (starting population)
r = the annual growth rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, let's assume that the animals reproduce once per year (n = 1), and the annual growth rate is 25% (r = 0.25). We can plug in these values into the formula and calculate the population after 100 years (t = 100).
A = 2(1 + 0.25/1)^(1*100)
A = 2(1 + 0.25)^100
A ≈ 2(1.25)^100
A ≈ 2 * 9.3132257461548
Therefore, after 100 years of a 25% annual growth rate, starting with two animals, the estimated population total would be approximately 18.6264514923096. Note that this is an approximate value because of rounding.