A culture of a certain bacteria doubles every hour at 9 AM there were already 120 bacteria, which equation represents the number of bacteria in at 8 AM. How many bacteria were there?
We can set up an exponential equation to represent the growth of the bacteria. Let's denote the number of bacteria at time t as N(t). Since the culture is doubling every hour, the exponential equation can be written as follows:
N(t) = N₀ * (2^t)
where N₀ is the initial number of bacteria and t is the number of hours that have elapsed.
Since at 9 AM (t = 0), there were already 120 bacteria, we can substitute those values into the equation:
120 = N₀ * (2^0)
120 = N₀ * 1
N₀ = 120
Now we know the initial number of bacteria. We can substitute this value into the equation and solve for t = -1 (8 AM):
N(-1) = 120 * (2^(-1))
N(-1) = 120 * (1/2)
N(-1) = 60
Therefore, at 8 AM, there were 60 bacteria.
To find the number of bacteria at 8 AM, we need to work backwards from 9 AM and account for the doubling every hour.
Let's use the variable 'n' to represent the number of hours before 9 AM that we want to calculate the number of bacteria for.
We know that at 9 AM, there were 120 bacteria, so at 8 AM (1 hour before), the number of bacteria would be half of that. Therefore, the number of bacteria at 8 AM can be represented as:
120 * (1/2)^n
Now, we can substitute 'n' with the number of hours between 9 AM and 8 AM (which is 1):
120 * (1/2)^1 = 120 * 1/2 = 60
So, at 8 AM, there were 60 bacteria.
To find the number of bacteria at 8 AM, we need to go back one hour from 9 AM. Since the bacteria double every hour, we can work backwards by dividing the number of bacteria by 2.
Here's how we can do it step by step:
1) At 9 AM, there were 120 bacteria.
2) To find the number of bacteria at 8 AM, we need to divide 120 by 2, since it doubles every hour.
120 ÷ 2 = 60.
Therefore, there were 60 bacteria at 8 AM.