Final answer:
The relationship between the elapsed time t, in years, since Fred started studying the tree, and the number of its branches, Byear(t), is modeled by the function Byear(t) = 20 * (2.5)^t. This function represents exponential growth, where the number of branches increases rapidly over time.
Step-by-step explanation:
The relationship between the elapsed time t, in years, since Fred started studying the tree, and the number of its branches, Byear(t), is modeled by the function Byear(t) = 20 * (2.5)^t.
This function represents exponential growth, where the number of branches increases rapidly over time. The base of the exponential function is 2.5, meaning that the number of branches multiplies by 2.5 every year. The coefficient 20 determines the initial number of branches when Fred started studying the tree.
For example, if t = 0 (the start of Fred's study), then Byear(t) = 20 * (2.5)^0 = 20, indicating that there were 20 branches at the beginning. If t = 1 (after 1 year), then Byear(t) = 20 * (2.5)^1 = 50, meaning that the number of branches increased to 50 after the first year.