Question: Consider a population that grows according to the explicit function \[ L_n = 8 + 35n. \] What is…

Consider a population that grows according to the explicit function \[ L_n = 8 + 35n. \]

What is the common difference for this arithmetic sequence? \[ d = \boxed{\phantom{0}} \]

What is the initial population? \[ L_0 = \boxed{\phantom{0}} \]

Solution

We are given the explicit function for population growth: \[ L_n = 8 + 35n \] The general form of an arithmetic sequence is: \[ L_n = L_0 + nd \] By comparing the two equations, we can identify the initial population and the common difference. \[ L_0 = 8 \] \[ d = 35 \] Therefore, the initial population \( L_0 \) is 8 and the common difference \( d \) is 35.