Let f(x) = (x − 3)^5 and x0 is not equal to 3. For each n ≥ 0, determine xn+1 from xn by using Newton’s method for finding the root of the equation f(x) = 0. Show that the sequence {xn} converges to 3 linearly with rate 4/5.

Suppose that the spread of a disease through the student body at an isolated college campus can be modeled by 10,000 y : 1 + 9999e-0.95t where y is the total number affected at time t (in days). Find the rate of change of y. 94990500e-0.95t 1 + 9999e-0.95t)