Answer :
We know that the water is evaporating at a rate of 5%, this means that the water amoun is decreasing. Since the rate at which this is happening is constant we can use an exponential function of the form:
[tex]y=A(1-r)^t[/tex]where A is the original amount of water, r is the rate in decimal form and t is the number of days. Plugging the initial amount and the rate we have that:
[tex]\begin{gathered} y=18800(1-0.05)^t \\ y=18800(0.95)^t \end{gathered}[/tex]Hence the amount of water after t days can be found by the expression:
[tex]y=18800(0.95)^t[/tex]Once we know the expression we plug the number of days we want to know, in this case nine, then we have:
[tex]\begin{gathered} y=18800(0.95)^9 \\ y=11849 \end{gathered}[/tex]Therefore, after nine days the pool has 11849 gallons of water.