1. Use the result of Exercise 2 to make a conjecture about the rate of growth of y1 = ex and y = xn, where n is a natural number and x approaches ∞.
2. Use the results of Exercises 2 and 3 to describe what is implied when it is stated that a quantity is growing exponentially.
3. Given the exponential function f (x) = ax show that
(a) f (u + v) = f (u) . f (v)
(b) f (2x) = [f (x)]2.