A lab is growing bacteria in a culture dish. The amount of bacteria in the dish doubles every 3 hours. Initially, there are 500 bacteria in the dish. How many are in the dish after 9 hours?
My answer: 4000
-(5)^-1
My answer: -1/5
Your answers are correct!
If there are initially 4000 bacteria in a culture, and the number of bacteria double each hour, the number of
bacteria after t hours can be found using the formula n= 4000(2t). How many bacteria will be present after
9 hours?
To find the number of bacteria in the dish after 9 hours, let's break it down step by step:
1. We know that the amount of bacteria in the dish doubles every 3 hours.
2. Since the initial number of bacteria is 500, we can divide the 9-hour period into three 3-hour intervals.
3. After the first 3 hours, the number of bacteria doubles from 500 to 1000.
4. After the second 3 hours (totaling 6 hours), the number of bacteria doubles again from 1000 to 2000.
5. Finally, after the last 3 hours (totaling 9 hours), the number of bacteria doubles once more from 2000 to 4000.
Therefore, the number of bacteria in the dish after 9 hours is 4000.
To find the number of bacteria in the dish after 9 hours, we need to use the exponential growth formula.
The formula for exponential growth is: A = P * (1 + r)^t
Where:
A = final amount
P = initial amount
r = growth rate (as a decimal)
t = time (in this case, hours)
In this case, the initial amount (P) is 500 bacteria, and the growth rate (r) is one because the amount of bacteria doubles every 3 hours. So, r = 1.
To find the time (t) after 9 hours, we divide 9 by the growth rate of 3 hours: t = 9 / 3 = 3.
Now, we can substitute these values into the formula and solve for the final amount (A):
A = 500 * (1 + 1)^3
A = 500 * 2^3
A = 500 * 8
A = 4000
So, after 9 hours, there would be 4000 bacteria in the dish. Therefore, the correct answer is 4000.