Question

The water in a pool is evaporating at a rate of 5% per day. If the pool has 18,800gallons in it today, how many gallons will it have in 9 days? Round your answer to thenearest whole number, if necessary.

Answer 1

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:

`y=A(1-r)^t`

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:

`\begin{gathered} y=18800(1-0.05)^t \\ y=18800(0.95)^t \end{gathered}`

Hence the amount of water after t days can be found by the expression:

`y=18800(0.95)^t`

Once we know the expression we plug the number of days we want to know, in this case nine, then we have:

`\begin{gathered} y=18800(0.95)^9 \\ y=11849 \end{gathered}`

Therefore, after nine days the pool has 11849 gallons of water.