The scenario with 1 death, 5 births, 3 immigration, and 7 emigration is the one that would keep the population growth of cheetahs the same in 2013.
To keep the population growth of cheetahs the same in 2013, the total number of births, deaths, immigration, and emigration should balance out.
Let's calculate the net change for each scenario:
4 deaths, 7 births, 2 immigration, 6 emigration
Net change = (7 - 4) + 2 - 6 = 3 - 4 = -1
3 deaths, 6 births, 5 immigration, 7 emigration
Net change = (6 - 3) + 5 - 7 = 3 - 2 = 1
5 deaths, 2 births, 8 immigration, 3 emigration
Net change = (2 - 5) + 8 - 3 = -3 + 5 = 2
1 death, 5 births, 3 immigration, 7 emigration
Net change = (5 - 1) + 3 - 7 = 4 - 4 = 0
To keep the population growth the same, the net change should be zero. Therefore, the scenario with 1 death, 5 births, 3 immigration, and 7 emigration is the one that would keep the population growth of cheetahs the same in 2013.