Final answer:
Forest B, starting with a lower initial population than Forest A, boasts a greater yearly growth rate that ultimately leads to it having a higher population than Forest A after 50 years.
Step-by-step explanation:
Let's compare the population growth of both forests. Forest A starts with a higher initial population (105 trees) than Forest B (87 trees). However, Forest B is growing at a faster yearly rate (2.9%) than Forest A (2.5%). Therefore, over time, the population of Forest B will increase more rapidly.
To determine which forest will have a greater number of trees after 50 years, we can substitute t=50 in both functions. A(50) = 105(1.025)^50 and B(50) = 87(1.029)^50. Calculating these values, we find that Forest B will have a greater number of trees after 50 years. The exact number by which Forest B exceeds Forest A can be found by subtracting A(50) from B(50).
This calculation illustrates how an initially smaller population (Forest B) can overtake a larger population (Forest A) over time due to a higher growth rate.
Learn more about Exponential Growth