The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria triples every 30 sec. (Hint: The answer should contain q as well as n.)
q=bacteria
r=3 (triples)
60÷30=2 (60 sec. in one minute divided by 30 sec.)
Solution:
q(3 to the second power n)
Well, let's put on our bacteria math caps, shall we? If the amount of bacteria triples every 30 seconds, that means after every 30 seconds, we have three times the amount we started with. So, in 30 seconds, we have 3q bacteria.
Now, let's think about it. If it triples every 30 seconds, that means after 60 seconds (2 times 30), it would triple again, making it 3 times the amount we had at 30 seconds. So, after 60 seconds, we have 3 times 3q, which is 9q bacteria.
Are you following me so far? Great!
Now, after 90 seconds (3 times 30), it triples once more, making it 3 times the amount we had at 60 seconds. So, after 90 seconds, we have 3 times 9q, which is 27q bacteria.
See the pattern here? It keeps tripling every 30 seconds. So, after n minutes, which is equal to 60n seconds, the amount of bacteria would be 3 to the power of (2n) times q.
So, in short, the amount of bacteria after n minutes would be 3^(2n) * q. Keep multiplying by 3 every 30 seconds, and watch that bacteria population grow!
To find the amount of bacteria after n minutes with an initial amount of q bacteria that triples every 30 seconds, we need to convert the given time into seconds.
Since there are 60 seconds in 1 minute, we can calculate the total number of seconds:
Total seconds = n minutes * 60 seconds/minute
Next, we need to determine how many 30-second intervals are in the total number of seconds:
Number of intervals = Total seconds / 30 seconds
Finally, we can calculate the final amount of bacteria by multiplying the initial amount (q) by 3 raised to the power of the number of intervals:
Final amount of bacteria = q * (3^Number of intervals)
Therefore, the amount of bacteria after n minutes, given an initial amount of q bacteria that triples every 30 seconds, can be calculated using the formula:
Final amount of bacteria = q * (3^(n minutes * 60 seconds/minute / 30 seconds))
To determine the amount of bacteria after a certain amount of time, we need to consider that the bacteria triples every 30 seconds. Let's break down the problem step by step:
1. Determine the number of 30-second intervals in n minutes:
Since there are 60 seconds in a minute and 30 seconds in an interval, we know that there are (n * 60) / 30 intervals in n minutes. Let's call this value x.
2. Calculate the factor by which the bacteria multiplies in each interval:
Since the amount of bacteria triples every 30 seconds, the multiplication factor for each interval is 3.
3. Calculate the final amount of bacteria:
To calculate the final amount of bacteria, we multiply the initial amount, q, by the multiplication factor raised to the power of the number of intervals, x.
In summary, the formula to calculate the amount of bacteria after n minutes, given an initial amount q and a bacterial multiplication every 30 seconds by a factor of 3, is:
Final amount = q * (3^x)
where x = (n * 60) / 30
So, to get the final answer, plug in the values of q and n into the formula.
population doubles twice every minute. After n minutes,
a = q*3^(2n)