A colony of bacteria originally contains 900 bacteria. It doubles in size every 30 minutes. How many hours will it take the colony to contain 9000 bacteria?
After 30 minutes, the colony will contain 900 x 2 = 1800 bacteria.
After 60 minutes (2 x 30 minutes), the colony will contain 1800 x 2 = 3600 bacteria.
After 90 minutes (3 x 30 minutes), the colony will contain 3600 x 2 = 7200 bacteria.
After 120 minutes (4 x 30 minutes), the colony will contain 7200 x 2 = 14400 bacteria.
Therefore, it will take 2 hours (120 minutes) for the colony to contain 9000 bacteria.
900(2^t) = 9000 , were t is the number of 1/2 hours
2^t = 10
t log2 = log 10
t =1/log2 = 3.322 half hours
t = 1.67 hours or 1 hours and 40 minutes
To solve this problem, we can use the concept of exponential growth.
Let's figure out how many times the colony doubles in size to reach 9000 bacteria.
Original number of bacteria = 900
Target number of bacteria = 9000
9000 / 900 = 10
So, the colony needs to double in size 10 times to reach 9000 bacteria.
Since the colony doubles in size every 30 minutes, the total time taken can be calculated by multiplying the doubling time (30 minutes) by the number of times it needs to double (10 times).
Total time = 30 minutes × 10 = 300 minutes
To convert minutes to hours, divide the total time by 60.
Total time = 300 minutes / 60 = 5 hours
Therefore, it will take 5 hours for the colony to contain 9000 bacteria.
To solve this problem, we can use the concept of exponential growth. The number of bacteria in the colony doubles every 30 minutes, which means the growth rate is 2.
Let's break down the problem step by step:
1. We start with 900 bacteria.
2. After 30 minutes, the number of bacteria doubles to 2 * 900 = 1800.
3. After another 30 minutes, the number of bacteria doubles again to 2 * 1800 = 3600.
4. We continue this doubling process until we reach or exceed 9000 bacteria.
To calculate how many times the bacteria doubles, we can use the formula:
n = log(base 2) (9000/900)
Here, "n" represents the number of times the bacteria doubles.
Using a calculator or math software, we find that n is approximately 3.17.
Since each doubling takes 30 minutes, we can calculate the total time required as follows:
total time = n * 30 minutes
total time = 3.17 * 30 minutes
The total time is approximately 95.1 minutes.
To convert this to hours, divide the total time by 60:
total time = 95.1 minutes / 60
The total time is approximately 1.6 hours.
Therefore, it will take approximately 1.6 hours for the colony to contain 9000 bacteria.