Two people are initially diagnosed with a virus which multiplies every 8 hours. After 2 days, there are 8192 people infected with the virus. What is the growth rate of the virus?(1 point)

Question

Responses

171
171

8
8

2
2

4

Answer 1

To find the growth rate of the virus, we can use the information provided about the initial number of infections and the total number of infections after 2 days.

1. Determine the duration in hours:

   • 2 days = 2 days * 24 hours/day = 48 hours.

2. Determine how many 8-hour periods are there in 48 hours:

   • 48 hours / 8 hours = 6 periods.

3. Calculate the total infections after the periods:

   • The initial number of infected people is 2.
   • The formula for exponential growth is given by: \[ N = N_0 \times r^t \] where \( N \) is the final number of people infected, \( N_0 \) is the initial number, \( r \) is the growth factor, and \( t \) is the number of periods.

   Substituting our numbers into the formula: \[ 8192 = 2 \times r^6 \]

4. Isolate \( r^6 \): \[ r^6 = \frac{8192}{2} = 4096 \]

5. Calculate \( r \): We know that \( 4096 = 2^{12} \) (since \( 2^{12} = 4096 \)). Therefore, we can write: \[ r^6 = 2^{12} \] Taking the sixth root of both sides: \[ r = 2^{12/6} = 2^2 = 4. \]

Thus, the growth rate of the virus is 4.