Questions: After a hurricane, a disease similar to cholera (but more contagious) has appeared in a town located in the Mississippi Delta region. Twenty-five cases are detected, and every 6 hours the number of infections doubles. The virus is airborne and very contagious. What type of sampling is used? A. Cluster sampling is used: take the disaster area as divided into grids and then randomly sample grids B. Cluster sampling is used: divide the disaster into grids and then randomly sample people from each grid C. Stratified sampling is used: since more than one area is divided into grids and samples are taken from each D. Standard sampling is used: since the disaster area is divided into grids and then samples are taken from each grid

Solution Steps

The question involves a scenario where the number of infections doubles every 6 hours. To find the number of infections after a certain period, we can use the formula for exponential growth: \( N(t) = N_0 \times 2^{t/T} \), where \( N_0 \) is the initial number of cases, \( t \) is the time elapsed, and \( T \) is the doubling time (6 hours in this case).

We start with an initial number of cases, \( N_0 = 25 \). The number of infections doubles every \( T = 6 \) hours.

We want to find the number of infections after \( t = 24 \) hours.

Using the formula for exponential growth, we have:

\[ N(t) = N_0 \times 2^{\frac{t}{T}} \]

Substituting the known values:

\[ N(24) = 25 \times 2^{\frac{24}{6}} \]

Calculating the exponent:

\[ \frac{24}{6} = 4 \]

Thus, we can rewrite the equation as:

\[ N(24) = 25 \times 2^4 \]

Calculating \( 2^4 \):

\[ 2^4 = 16 \]

Now substituting back into the equation:

\[ N(24) = 25 \times 16 = 400 \]

Final Answer