A culture of a certain bacteria doubles every hour At 9 * 0a .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)
The equation that represents the number of bacteria, n, at any given time t is:
n = 120 * (2^(t - 9))
To find the number of bacteria at 8 a.m. (t = 8), we substitute t = 8 into the equation:
n = 120 * (2^(8 - 9))
n = 120 * 2^(-1)
n = 120 * 0.5
n = 60
Therefore, there were 60 bacteria at 8 a.m.
To determine the equation that represents the number of bacteria at 8:00 am, we need to first identify the time difference between 8:00 am and 9:00 am. Since we are going back one hour, the time difference is -1 hour.
The equation for the exponential growth of bacteria can be expressed as:
n = P * (2^t/h),
where:
n is the final number of bacteria,
P is the initial number of bacteria,
t is the time difference, and
h is the doubling time.
In this case, the initial number of bacteria at 9:00 am is 120, and the doubling time is 1 hour. The time difference between 8:00 am and 9:00 am is -1 hour.
Substituting these values into the equation, we have:
n = 120 * (2^(-1/1)) = 120 * (1/2) = 60.
Therefore, the equation representing the number of bacteria at 8:00 am is n = 60, and the number of bacteria at that time is 60.
To find the equation representing the number of bacteria at 8:00 a.m., we need to determine the number of hours that have passed since 9:00 a.m.
From 9:00 a.m. to 8:00 a.m. the next day, 23 hours have passed.
Since the culture of bacteria doubles every hour, we can use the equation: n = 120 * (2^t), where n represents the number of bacteria and t represents the number of hours passed.
Using this equation, when t = 23, we can calculate the number of bacteria at 8:00 a.m.
n = 120 * (2^23)
n = 120 * (2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2)
n = 120 * 8388608
n = 1,006,332,160
Therefore, the equation representing the number of bacteria at 8:00 a.m. is n = 1,006,332,160, and there were approximately 1,006,332,160 bacteria present.