In a small town. 4 residents came down with a mysterious virus. Two weeks (14 da

Question

In a small town. 4 residents came down with a mysterious virus. Two weeks (14 days) later, there were 20 total cases. Assume the number of people infected with the virus is growing exponentially. Give the function that can be used to find the number of residents affected with the virus / days after the first 4 residents were identified. What is the doubling time for the number of affected residents? If the number of affected residents continues to grow exponentially, when will 200 cases have been reported?

Explanation / Answer

A'(t) = k e^t

A(t) = k e^t + C

A(0) = 4 =>k + C = 4

A(14) = 20 => k e^14 +C = 20 => k (e^{14}-1) = 16

k = 16/(e^14 - 1 ) C = 4 - 16/(e^14 - 1 )

A(t ) = K e^t + 4-K

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