Question

Multiple Choice If a flu is spreading at the rate of \(P(t)=\frac{150}{1+e^{4-t}}\) which of the following is the initial number of persons infected? \(\begin{array}{llll}{\text { (A) } 1} & {\text { (B) } 3} & {\text { (C) } 7} & {\text { (D) } 8} & {\text { (E) } 75}\end{array}\)

Short answer

The initial number of infected persons is approximately 3 (option B)

Step-by-step solution

Substituting t = 0 into the function

To find the initial number of persons infected, we substitute \(t=0\) into the function. Our function becomes \(P(0)=\frac{150}{1+e^{4-0}}\).

Simplifying the function

Simplifying the expression, we have \(P(0)=\frac{150}{1+e^{4}}\).

Calculating the value of P(0)

Using a calculator or a mathematical software to calculate the value of \(e^4\) and compute the division, we find that \(P(0)=150/(1+e^4)=150/(1+54.59815003) \approx 2.73\). Based on the answer choices, the closest number to our result is 3.