Suppose you were studying a species that has a population cycle of about ten years. how long would you need to study the species to determine if its population size were declining?

The number of years it will take you to have completed studied an organism that has a life cycle of 10 years, is 15 or more than that. This is because you cannot just easily derived to a conclusion without controlling the environmental aspects of the experiments. 

The answer is the second choice,  the rates at which criminals are rehabilitated into society after their sentencing

What exactly are you asking? i’d love to , explain, what you are asking : )