A population of animals starts at 212,000 and grow continuously at 5% per year to 386,289. How long does it take to achieve this growth?
To find out how long it takes to achieve this growth, we can use the continuous growth formula:
A = P * e^(rt)
Where:
A = final population
P = initial population
e = Euler's number (approximately 2.718)
r = growth rate
t = time (in years)
In this case, the initial population (P) is 212,000, the final population (A) is 386,289, and the growth rate (r) is 5%.
386,289 = 212,000 * e^(0.05t)
Dividing both sides of the equation by 212,000, we get:
1.821 = e^(0.05t)
Take the natural logarithm (ln) of both sides:
ln(1.821) = 0.05t
Now, divide both sides of the equation by 0.05:
t = ln(1.821) / 0.05
Using a calculator, we find:
t ≈ 11.390
Therefore, it takes approximately 11.390 years to achieve this growth.