The penguin population on an island is modeled by a differentiable function P of time t, where P(t) is the number of penguins and t is measured in years (0 ≤ t ≤ 40). There are 100,000 penguins on the island at time t = 0. What is the rate of change of the penguin population on the island at time t = 0?
A) 75,000 penguins per year
B) 100,000 penguins per year
C) 125,000 penguins per year
D) 150,000 penguins per year