Review 1. A maintenance worker in a factory notices that a water tank is
Day Volume of Water (L)
leaking. She records the amount of water in the tank each day 1
16,000
in a table,
2
12,000
a. Write a recursive formula to represent the pattern shown in 3
9,000
the table. What predictions does this formula make for the
4
6,750
amount of water in the tank on the 5th day?
b. Write an explicit formula to represent the pattern shown in the table. What predictions does this
formula make for the amount of water in the tank on the 10th day?

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