A captive population of monkeys made up of 130 individuals in the year 1966 has a size of 520 in the year 2010.Assuming that the rate of population growth was constant,the doubling time of this population was _______ years.

Question

Quizplus · Accepted Answer

The formula for calculating the doubling time is:
doubling time (t) = (ln 2 / r) * t
where ln 2 is the natural logarithm of 2, r is the annual growth rate, and t is the number of years.
To find the annual growth rate, we can use the formula:
Nt = No * e^(rt)
where Nt is the final population, No is the initial population, e is the natural log base (approximately 2.718), r is the annual growth rate, and t is the number of years.
We can rearrange this formula to solve for r:
r = (ln Nt - ln No) / t
Plugging in the given values:
No = 130, Nt = 520, t = 44
r = (ln 520 - ln 130) / 44 = 0.035
Now we can calculate the doubling time:
t = (ln 2 / 0.035) * t = 22 years

A Captive Population of Monkeys Made Up of 130 Individuals