A population of bacteria is estimated to increase by 12% every 24 hours. The population was 2000 at midnight on Friday. What was the population (to the nearest whole number) by midnight the following Wednesday?

A population of bacteria is estimated to increase by 12% every 24 hours. The population was 2000 at midnight on Friday. What was the population (to the nearest whole number) by midnight the following Wednesday?

Answer

To find the population of the bacteria by midnight Wednesday, we first need to determine the number of days between Friday midnight and Wednesday midnight. 1. Count the days from Friday to Wednesday: - Friday to Saturday: 1 day - Saturday to Sunday: 1 day - Sunday to Monday: 1 day - Monday to Tuesday: 1 day - Tuesday to Wednesday: 1 day Total days = 5 days. 2. The population increases by 12% each day. This can be expressed as a growth factor of 1.12. 3. The population at midnight on Friday ( P = 2000) will grow over 5 days, so we use the formula: Final Population = Initial Population × (Growth Factor ^ Number of Days) Final Population = 2000 × (1.12 ^ 5) 4. Calculate (1.12 ^ 5): - (1.12 ^ 5) ≈ 1.7623 (using a calculator) 5. Now calculate the final population: Final Population = 2000 × 1.7623 ≈ 3524.6 6. Rounding to the nearest whole number gives us: Final Population ≈ 3525. Therefore, the population of bacteria by midnight Wednesday is approximately 3525.