**Explanation:**

**Entropy in an Isolated System:**

Entropy is a measure of the disorder or randomness in a system. In an isolated system, the total entropy remains constant unless there is an exchange of energy or matter with the surroundings.

**Change in Entropy:**

According to the second law of thermodynamics, the total entropy of an isolated system tends to increase over time. This means that the system becomes more disordered or random as time passes. Therefore, the entropy of an isolated system continuously increases.

**Equilibrium State:**

At the state of equilibrium, the system has reached a state of maximum entropy. This means that the system is in the most disordered or random state possible. In this state, there is no further tendency for the entropy to increase. Therefore, the entropy at the state of equilibrium is at its maximum value.

**Answer Explanation:**

Based on the above information, we can conclude that the correct answer is option B: "increases, maximum." The entropy of an isolated system continuously increases over time and reaches its maximum value at the state of equilibrium.

Other options can be ruled out:

- Option A: "decreases, minimum" is incorrect because entropy in an isolated system does not decrease over time. It either remains constant or increases.
- Option C: "increases, minimum" is incorrect because the entropy at the state of equilibrium is at its maximum value, not minimum.
- Option D: "decreases, maximum" is incorrect because the entropy of an isolated system does not decrease over time. It either remains constant or increases.

In summary, the entropy of an isolated system continuously increases and reaches its maximum value at the state of equilibrium.