A scientist observes a population of bacteria in a petri dish. The population grows exponentially, doubling every 2hours. After 4hours of observation, there are about 6,000 bacteria.
Which equation can you use to estimate n, the number of bacteria that were originally in the petri dish?
To estimate the number of bacteria that were originally in the petri dish, we can use the formula for exponential growth:
N = N0 * 2^(t/h)
Where:
N is the final population size after time t
N0 is the initial population size (the number of bacteria originally in the petri dish)
t is the time period (in this case, 4 hours)
h is the time it takes for the population to double (in this case, 2 hours)
We are given that after 4 hours, there are about 6,000 bacteria. So we can plug in these values into the equation and solve for N0:
6,000 = N0 * 2^(4/2)
Simplifying the equation:
6,000 = N0 * 2^2
6,000 = 4N0
Dividing both sides of the equation by 4:
6,000/4 = N0
1,500 = N0
Therefore, the equation to estimate n, the number of bacteria that were originally in the petri dish, is:
N0 = 1,500