1. 10 points) The Black-tailed prairie dog was decimated in Arizona in the 1960s due to a disease. A large part of the population, which was at carrying capacity, was killed. Only 10% survived. How long would it take with a regrowth rate of 2% to back to the carrying capacity? How many years will it take for the same situation if we double the regrowth due to improved ecosystems and double the initial amount of prairie dogs by importing prairie dogs from New Mexico? Note that you do not know the absolute carrying capacity of the population, but you can use the relative carrying capacity, where K=100% for a fully recovered population).

using the logistic growth model P_t+1 = P_t + rP_t (1 - P_t / K)

my ending answer is 41 years and 0.425 months