if a butterfly populatuon grows by 10% per annum, how many years will it take its population to double

Answer 1

To find out how long it will take for the butterfly population to double, we can use the formula for exponential growth:

Population after t years = Initial population * (1 + growth rate)^t

Let's assume the initial population is 1 (for simplicity). If the population grows by 10% per annum, the growth rate would be 0.1 (10% expressed as a decimal).

So, the formula becomes:

2 = 1 * (1 + 0.1)^t

Solving for t:

2 = (1.1)^t
2 = 1.1^t

Taking the natural logarithm of both sides:

ln(2) = ln(1.1^t)
ln(2) = t * ln(1.1)

t = ln(2) / ln(1.1)
t ≈ 6.72

Therefore, it will take approximately 6.72 years for the butterfly population to double.