In a laboratory, a certain culture of bacteria doubles every hour. If there are originally 20 bacteria in the culture, how many are present after 10 hours? 11 hours?
amount = 20 (2)^t
plug in t = 10, then t = 11
or do it the long way:
now -- 20
after 1 hour -- 40
after 2 hours -- 80
....
To calculate the number of bacteria present after a certain number of hours, we can use the formula:
Number of bacteria = Initial number of bacteria * (growth rate)^(number of hours)
Given:
Initial number of bacteria = 20
Growth rate = 2 (as the bacteria double every hour)
Calculating for 10 hours:
Number of bacteria after 10 hours = 20 * (2)^10
= 20 * 1024
= 20,480
Therefore, there are 20,480 bacteria present after 10 hours.
Calculating for 11 hours:
Number of bacteria after 11 hours = 20 * (2)^11
= 20 * 2048
= 40,960
Therefore, there are 40,960 bacteria present after 11 hours.
To find the answer, we need to use the formula for exponential growth: A = P * (1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate, and t is the time in hours.
In this case, the initial amount is 20 bacteria, and they double every hour, so the growth rate (r) is 2.
Let's calculate the number of bacteria after 10 hours:
A = 20 * (1 + 2)^10
A = 20 * 3^10
A = 20 * 59049
A ≈ 1,180,980
Therefore, after 10 hours, there would be approximately 1,180,980 bacteria in the culture.
Now, let's calculate the number of bacteria after 11 hours:
A = 20 * (1 + 2)^11
A = 20 * 3^11
A = 20 * 177,147
A = 3,542,940
Therefore, after 11 hours, there would be 3,542,940 bacteria in the culture.