Final answer:
The number of COVID-19 cases quadrupling every 3 days from an initial 1,000 cases results in an exponential growth, leading to an expected 1,048,576,000 cases after one month.
Step-by-step explanation:
The question involves an exponential growth model in the context of the COVID-19 pandemic, where the number of cases is quadrupling every 3 days. Starting with 1,000 cases, the calculation of the number of cases after one month (approximately 30 days) requires the use of the formula for exponential growth.
To find the number of times the cases quadruple in one month, we divide the total number of days in one month (30) by the number of days it takes to quadruple (3), which gives us 30/3 = 10. Therefore, the initial number of cases will quadruple 10 times in one month.
We can express this calculation using the formula A = P(4)^((t/h)), where A is the amount of cases after t days, P is the initial number of cases, 4 is the factor by which the cases quadruple, t is the total number of days, and h is the period in days for the cases to quadruple.
Plugging in the values we get A = 1000(4)^((30/3)) = 1000(4)^(10). Computing (4)^(10) gives us 1,048,576. Therefore, after one month, there would be A = 1000 * 1,048,576 = 1,048,576,000 cases expected, assuming the rate of quadrupling remains constant.