A culture of a certain bacteria doubles every hour . At 9:00 a.m. there were already were already 120 bacteria. Which equation represents the number of bacteria. , n, at 8:00 AM? How many bacteria’s were there?
Let's assume that n represents the number of hours since 8:00 a.m.
Since the bacteria doubles every hour, we can use the equation:
n = 9 - x
Where x represents the number of hours between 8:00 a.m. and 9:00 a.m.
To find the value of x, we subtract 8:00 a.m. from 9:00 a.m.
9:00 a.m. - 8:00 a.m. = 1 hour
Since there was 1 hour between 8:00 a.m. and 9:00 a.m., we substitute x = 1 in the equation:
n = 9 - 1
n = 8
The equation that represents the number of bacteria at 8:00 a.m. is n = 8.
Since n = 8, the number of bacteria at 8:00 a.m. is 8.
To find the number of bacteria at 8:00 AM, we need to determine how many hours have passed from 9:00 AM to 8:00 AM.
Since there are 60 minutes in an hour, there are 60 x 60 = 3600 seconds in an hour.
From 9:00 AM to 8:00 AM the next day, there are 24 hours. Therefore, the number of hours from 9:00 AM to 8:00 AM is 24 - 1 = 23 hours.
Since the culture of bacteria doubles every hour, we can use the exponential growth formula:
n = P × (2^t),
where:
- n is the number of bacteria at a specific time,
- P is the initial population of bacteria,
- t is the number of time units (hours in this case) that have passed.
Let's calculate the equation for the number of bacteria at 8:00 AM:
n = 120 × (2^23).
Using the exponential function, we can calculate the number of bacteria:
n ≈ 120 × 8,388,608 ≈ 1,006,633,960.
Therefore, there were approximately 1,006,633,960 bacteria at 8:00 AM.
To determine the number of bacteria, n, at 8:00 AM, we need to work backward using the information provided.
Given:
- The bacteria population doubles every hour.
- At 9:00 AM, there were already 120 bacteria.
Let's start by finding how many hours have passed from 9:00 AM to 8:00 AM. Since there is a difference of 1 hour, we know that 1 hour has passed.
Now, since the bacteria population doubles every hour, we can write the equation:
n = 120 * 2^h
Where n is the number of bacteria and h is the number of hours since 9:00 AM.
Since we want to find the number of bacteria at 8:00 AM, we substitute h = 1 into the equation:
n = 120 * 2^1
n = 120 * 2
n = 240
Therefore, the equation that represents the number of bacteria, n, at 8:00 AM is n = 240. And at that time, there were 240 bacteria.