he following problems add in a minimal threshold value for the species to survive, T, which changes the differential equation to
P't = rp(1-P/K) (1-T/P)

Bengal tigers in a conservation park have a carrying capacity of 100 and need a minimum of 10 to survive. If they grow in population at a rate of 1% per year, with an initial population of 15 tigers, solve for the number of tigers present.