Dr. Schmidt recorded a count of 100 patients infected with a disease After 15 weeks, they counted 212 patients. Assuming the count of patients infected grows at a continuous rate, write an exponential model for this situation in terms of t.the number of weeks passed. Round to two decimal places.when necessary. Show your work here Hint: To add an exponent (x^y) type "exponent" or press "A" I A(t)=

To write an exponential model for the situation, we can use the formula for continuous growth: where:- \( A(t) \) is the amount at time ,- is the initial amount,- is the continuous growth rate,- is the time in weeks,- is the base of the natural logarithm.Given:- Initial count ,- Count after 15 weeks \( A(15) = 212 \).We need to find the growth rate . Using the information provided: First, solve for : Now, take the natural logarithm of both sides to solve for : Calculate : Now, substitute and back into the exponential model: So, the exponential model is: