Problem ER12

The following table reports the percent changes between one year and the next for the chamois population of Valparadiso (measured whenever the provincial administration has got the funds to conduct the relevant censuses)

Year	1985	1986	1988	1991	1992	1994	1997	1998	2001
Annual increase	105%	98%	92%	112%	107%	88%	93%	101%	97%

Assume that the population has a Malthusian dynamics and estimate both the instantaneous and the finite rate of demographic increase of the chamois.

The nearby Department of Animal Ecology has independently estimated that the population dynamics is driven by a multiplicative noise. The logarithm of such a noise is approximately white, Gaussian, with null mean value and variance $\sigma_\varepsilon^2$ equal to $6 \cdot 10^{-4}$. In 2014, the provincial administration has counted 350 chamois in Valparadiso. Calculate the probability that the chamois numbers drop below 200 individuals in 2040. To this end use the table reporting the areas of a standard normal distribution available online (e.g. on Wikipedia).