1. **State the problem:** We are given the function for the number of words remembered after $t$ days: $$w(t) = 100 \times (1 - 0.1t)^2, \quad 0 \leq t \leq 10.$$ We need to find the rate at which the person forgets words 2 days after learning, which means finding the derivative $w'(t)$ at $t=2$. 2. **Find the derivative $w'(t)$:** $$w(t) = 100 (1 - 0.1t)^2.$$ Using the chain rule, $$w'(t) = 100 \times 2(1 - 0.1t) \times (-0.1) = 100 \times 2 \times (1 - 0.1t) \times (-0.1).$$ Simplify: $$w'(t) = 100 \times 2 \times (-0.1) \times (1 - 0.1t) = -20 (1 - 0.1t).$$ 3. **Evaluate $w'(t)$ at $t=2$:** $$w'(2) = -20 (1 - 0.1 \times 2) = -20 (1 - 0.2) = -20 \times 0.8 = -16.$$ 4. **Interpretation:** The negative sign indicates the person is forgetting words. The rate of forgetting 2 days after learning is 16 words per day. **Final answer:** $$\boxed{-16}$$ words per day (the person forgets words at this rate 2 days after learning).