Question

Consider a swimming pool that initially contains 200 gallons of water. Water is added to the pool using a 40 gallon bucket, one full bucket every minute.

(a) Write an equation for the difference W(n+1)âW(n), which models this situation, where W(n) is the amount of water gallons as function of the number of minutes.
(b) Write the initial condition for the differentce equation above.W(0)= _______.

Answer 1

(a) W(n+1) = W(n) + 40

(b) W(0) = 200

Explanation:

(a) Since for every minute, a full 40 gallon bucket is poured into the swimming pool, this means in the following minute the pool has 40 gallon more water than the current time

Therefore W(n+1) = W(n) + 40

(b) Initially the pool contains 200 gallons of water. So the initial condition for the difference equation is

W(0) = 200