Applications
4. Erin is traveling abroad this summer and would like to have a bit of spending cash while
she's overseas. She has 100 dollars already saved and she plans on saving 40 dollars a month.
(a) Fill out the table below for the amount of money she saves as a function of how many
months she has been saving.
m
m1 2 3 4
a(m) 140
(b) Give a recursive definition for the sequence a(m). Don't forget to give an initial value.

Ateam of runners is needed to run a 1 2 -mile relay race. if each runner must run 1 4 mile, how many runners will be needed?

How does the graph of y = 3x compare to the graph of y = 3-x?

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0