Question

swine flu is attacking porkopolis. the function below determines how many people have swine where t represents the time in days and s represents the number of people in thousands.\\( s(t) = 9t - 4 \\)\
a) find s(4).\
b) what does s(4) mean in the context of the problem?\
c) find t when s(t) = 23.

Explanation:

Part (a)

Step1: Substitute \( t = 4 \) into \( s(t) \)

We have the function \( s(t)=9t - 4 \). To find \( s(4) \), we replace \( t \) with \( 4 \) in the function. So we get \( s(4)=9\times4 - 4 \).

Step2: Calculate the value

First, calculate \( 9\times4=36 \), then subtract \( 4 \): \( 36 - 4 = 32 \).

In the context of the problem, \( t \) is time in days and \( S(t) \) is the number of people (in thousands) with swine flu. So \( S(4) \) means that after 4 days, the number of people (in thousands) who have swine flu in Porkopolis. From part (a), we know \( S(4) = 32 \), so it means that after 4 days, 32 thousand people have swine flu.

Step1: Set up the equation

We know that \( s(t)=9t - 4 \) and \( s(t) = 23 \). So we set up the equation \( 9t-4=23 \).

Step2: Solve for \( t \)

First, add 4 to both sides of the equation: \( 9t-4 + 4=23 + 4 \), which simplifies to \( 9t=27 \). Then divide both sides by 9: \( t=\frac{27}{9}=3 \).

Answer:

\( 32 \) (since \( S \) is in thousands, it means 32 thousand people)

Part (b)