Answer:20.79
Explanation:
[ N = N₀ \cdot 2^{(t / 10)} ]
Where:
(N) is the final population (which is 6 times the initial population).
(t) is the time in hours.
Given that the final population is 6 times the initial population, we have:
[ N = 6N₀ ]
Substitute this into the exponential growth equation:
[ 6N₀ = N₀ \cdot 2^{(t / 10)} ]
Solving for (t):
[ 6 = 2^{(t / 10)} ]
Taking the natural logarithm (ln) of both sides:
[ \ln(6) = \frac{t}{10} \cdot \ln(2) ]
Solving for (t):
[ t = 10 \cdot \frac{\ln(6)}{\ln(2)} ]
Now, let’s calculate the value of (t):
[ t \approx 20.79 \text{ hours} ]
Therefore, the bacteria population was two-fold approximately 20.79 hours ago from the present time.