Suppose you're studying Arabic and you need to learn a list of 200 new words. One theory says that you learn new vocabulary at a rate proportional to the number of words that you don't yet know. Let W be the number of words that you know, and let t be time in days. 1. Which of these differential equations correctly models this situation, and why? dW dt = kW dW dt = k(200 W) 2. Would the constant k be positive or negative in this context? Why? 3. Show that W = 200 - Ae-kt is a solution to the differential equation (A is a constant.). f