Question

Dr. Marin recorded a count of 60 patients infected with a disease. Assuming the count of patients infected grows at a rate of 3% per week, find the growth factor and write an exponential model for this situation in terms of t, the number of weeks passed.

Answer 1

To find the growth factor and write an exponential model for the given situation, we can use the Rule of 70 and the formula for exponential growth.

Step-by-step explanation:

To find the growth factor, we can use the Rule of 70. The growth rate is given as 3% per week. So, the doubling time would be 70 divided by the growth rate percentage, which is 70/3 = 23.33 weeks. This means that it takes approximately 23.33 weeks for the number of patients infected to double.

To write an exponential model in terms of t, the number of weeks passed, we can use the formula:

Count of patients infected = Initial Count * (1 + Growth Rate)t

Since the initial count is 60 and the growth rate is 3% per week, the exponential model would be:

Count of patients infected = 60 * (1 + 0.03)t