Quantitative Literacy Practice Exam

What will be the volume of a pool after 14 days if it starts with 19,800 gallons and evaporates at 2% per day?

1. 14,256 gallons

2. 15,000 gallons

3. 16,000 gallons

4. 13,500 gallons

The correct answer is: 14,256 gallons

To determine the volume of the pool after 14 days, given that it starts with 19,800 gallons and evaporates at a rate of 2% per day, we need to apply the concept of exponential decay. The formula to calculate the remaining volume after a certain number of days with a daily percentage decrease is: \[ V = V_0 \times (1 - r)^t \] Where: - \( V_0 \) is the initial volume, - \( r \) is the rate of evaporation (expressed as a decimal), and - \( t \) is the number of days. In this scenario: - The initial volume \( V_0 = 19,800 \) gallons, - The evaporation rate \( r = 0.02 \), - The time \( t = 14 \) days. Substituting in these values: \[ V = 19,800 \times (1 - 0.02)^{14} \] Simplifying the equation: \[ V = 19,800 \times (0.98)^{14} \] Now, calculating \( (0.98)^{14} \): \[ (0.98)^{14} \approx