I tried to answer this problem.
Jane was studying a penguin colony which had approximately 1000 penguins. Each year 20% die from natural causes. There are an equal number of males and females. One male and one female are a couple and each couple has one chick. How many penguins will be in the colony after 7 years? What formula would you use to determine the number of penguins?
I got around 210. I just used the usual decay formula but I am not sure if this is correct the part ""There are an equal number of males and females. One male and one female are a couple and each couple has one chick." makes me confused. Is it necessary or not?
$$P=1000(1-0.2)^7$$ $$P=209.7152$$
I think problem means for you to further assume that (1)"chick" becomes adult immediately next period, (2)"chick" is $\frac12$ probability male/female (3) all adults reproduce (4) they reproduce first before dying of natural cause before the end of the period.
Your answer only accounted for the decay rate and not the birth rate. Let $N_0=1000, N_t$ number of penguins after $t$ periods. In this case, $$N_t=N_{t-1}(1-0.2)(1+0.5)=N_0((0.8)(1.5))^t=1000(1.2)^7=3583.18$$ where $(1-0.2)$ death rate $(1+0.5)$ birth rate (every couple produces $1$ per period).