\[ P(t)=1,800(1.02)^{t} \] The function \( P \) gives the estimated number of marine mammals in a certain area, where \( t \) is the number of years since a study began. What is the best interpretation of \( P(0)=1,800 \) in this context? A) The estimated number of marine mammals in the area was 102 when the study began. B) The estimated number of marine mammals in the area was 1,800 when the study began. C) The estimated number of marine mammals in the area increased by 102 each year during the study. D) The estimated number of marine mammals in the area increased by 1,800 each year during the study.

The best interpretation of \( P(0)=1,800 \) in this context is: B) The estimated number of marine mammals in the area was 1,800 when the study began. This is because \( P(0) \) represents the value of the function at the start of the time period, indicating the initial population of marine mammals before any growth occurred. In mathematical modeling, such as this, the initial value often serves as a crucial baseline for understanding growth trends over time. By knowing \( P(0) \), researchers can project future populations and evaluate the impact of conservation efforts or environmental changes. This function can also be used in discussions related to marine biology and ecosystem management.