The water in a pool is evaporating at a rate of 5% per day. If the pool has 15,600 gallons in it today, how many gallons will it have in 11 days? Round your answer to the nearest whole number, if necessary. Answer How to enter your answer (opens in new window)

To solve this problem, we need to use the formula for exponential decay, which is:<br /><br />\[ A = P(1 - r)^t \]<br /><br />Where:<br />- \( A \) is the amount of water remaining after \( t \) days.<br />- \( P \) is the initial amount of water.<br />- \( r \) is the daily rate of evaporation (as a decimal).<br />- \( t \) is the number of days.<br /><br />Given:<br />- \( P = 15,600 \) gallons<br />- \( r = 0.05 \) (5% per day)<br />- \( t = 11 \) days<br /><br />Plugging these values into the formula:<br /><br />\[ A = 15,600 \times (1 - 0.05)^{11} \]<br />\[ A = 15,600 \times (0.95)^{11} \]<br /><br />Now, calculate \( (0.95)^{11} \):<br /><br />\[ (0.95)^{11} \approx 0.5667 \]<br /><br />Then multiply by the initial amount:<br /><br />\[ A \approx 15,600 \times 0.5667 \]<br />\[ A \approx 8,800 \]<br /><br />So, the pool will have approximately 8,800 gallons of water in 11 days.