Answer :
The bacteria population grows exponentially. After solving for the growth rate and applying it to 24 hours, there will be approximately 2681 bacteria in 1 day.
This problem involves exponential growth of a bacteria population. We can use the formula for population growth:
N(t) = N0 * ert
Where:
N(t) is the population size at time t
N0 is the initial population size
r is the growth rate
t is the time
Given:
N0 = 100 bacteria
N(t) after 8 hours = 300 bacteria
t = 8 hours
First, we need to solve for the growth rate r. Rearranging the formula for r:
300 = 100 * e8r
3 = e8r
Taking the natural logarithm on both sides:
ln(3) = 8r
r = ln(3) / 8
r ≈ 0.137
Now, we need to find the population size after 1 day (24 hours):
N(24) = 100 * e0.137*24
N(24) ≈ 100 * e3.288
N(24) ≈ 100 * 26.813
N(24) ≈ 2681.3
Therefore, there will be approximately 2681 bacteria in 1 day.
