Final answer:
The question asks for a reasonable domain of a population model since 1977. It is reasonable to set the domain starting from the year 1977 (t = 0) and extend it several decades into the future, where the model remains reliable, such as up to the year 2027 or 2077.
Step-by-step explanation:
The question deals with determining a reasonable domain for a population model function. Based on the information given, we can infer that the function P(t) represents the population in thousands, t years since 1977.
The domain of a function represents all the possible input values (t, in this case), which will give valid output values. Since we are dealing with real-life population data, the domain would naturally start from t = 0 (the year 1977). The upper limit of the domain would depend on how far into the future we wish to predict or until the model remains valid. Typically, demographic models change significantly over time due to various factors such as technological, environmental, or social changes. Hence, it is reasonable to set a domain that extends several decades into the future but not too far that the model becomes unreliable or irrelevant.
Considering these factors, a reasonable domain for P(t) might be from t = 0 (year 1977) up to t = 50 or t = 100, representing the years 2027 or 2077, respectively.