A culture of a certain bacteria doubles every hour. At 9:00 a.m, there were already 120 bacteria. Which equation represents the number of bacteria, n , at 8:00 a.m? How many bacteria were there?(1 point)
Let's assume the number of bacteria at 8:00 a.m is represented by n.
Since the bacteria doubles every hour, the number of bacteria at 9:00 a.m can be represented as 2n (twice the amount at 8:00 a.m).
We are given that at 9:00 a.m, there were already 120 bacteria. So we can set up the equation:
2n = 120
To find the number of bacteria at 8:00 a.m, we need to solve for n:
n = 120/2
n = 60
Therefore, there were 60 bacteria at 8:00 a.m.
To find the equation that represents the number of bacteria, n, at 8:00 a.m, we need to determine the number of hours between 8:00 a.m and 9:00 a.m.
Since we are going back in time, we need to count the number of hours in reverse. From 9:00 a.m to 8:00 a.m is a span of 1 hour.
To find the number of bacteria at 8:00 a.m, we can use the formula for exponential growth:
n = A × (2^h)
Where:
- n is the number of bacteria at 8:00 a.m
- A is the initial number of bacteria (120 at 9:00 a.m)
- h is the number of hours since 9:00 a.m (1 hour in this case)
Substituting the values into the formula, we get:
n = 120 × (2^1)
Simplifying, we have:
n = 120 × 2
n = 240
Therefore, the equation that represents the number of bacteria, n, at 8:00 a.m is n = 120 × 2, and there were 240 bacteria at that time.
To find the equation that represents the number of bacteria at 8:00 a.m., we need to determine the rate at which the number of bacteria doubles every hour.
We know that the culture doubles every hour, so the growth rate is 2. This means that for every hour that passes, the number of bacteria is multiplied by 2.
Now let's consider the time difference between 8:00 a.m. and 9:00 a.m., which is 1 hour. We know that by 9:00 a.m. there were already 120 bacteria, so we can divide this number by the growth rate of 2 to find the number of bacteria at 8:00 a.m.
120 bacteria / 2 = 60 bacteria
Therefore, the equation that represents the number of bacteria at 8:00 a.m. is:
n = 60
And the number of bacteria at 8:00 a.m. was 60.