Questions: Solve the problem. Suppose the number of people infected with a certain virus x days after beginning treatment can be described by f(x)=567 e^(-0.01957 x). How many people were infected initially? A) 1956 B) 567 C) 560 D) 1

Solve the problem. Suppose the number of people infected with a certain virus x days after beginning treatment can be described by f(x)=567 e^(-0.01957 x). How many people were infected initially? A) 1956 B) 567 C) 560 D) 1

Transcript text: Solve the problem. 15) Suppose the number of people infected with a certain virus $x$ days after beginning treatment can be described by $f(x)=567 e^{-0.01957 x}$. How many people were infected initially? A) 1956 B) 567 C) 560 D) 1

Solution

Solution Steps

To find the number of people infected initially, we need to evaluate the function $ f(x) $ at $ x = 0 $. This will give us the initial number of infected people.

Solution Approach

Evaluate the function $ f(x) $ at $ x = 0 $.
The result will be the initial number of infected people.

Step 1: Evaluate the Function at $ x = 0 $

To find the initial number of people infected, we evaluate the function $ f(x) = 567 e^{-0.01957 x} $ at $ x = 0 $: \[ f(0) = 567 e^{-0.01957 \cdot 0} = 567 e^{0} = 567 \cdot 1 = 567 \]

Step 2: Conclusion

The initial number of people infected with the virus is $ 567 $.