Question

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)
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**.