The doubling period of a bacteria culture is 35 minutes and it starts with 1400 bacteria. How many bacteria will there be after 3 hours? Round your answer to the nearest tenth.
2 = e^35 k
ln 2 = 35 k
k = .0198
so
a = 1400 e^.0198*3*60
a = 1400 e^3.565
a = 49,475.2
thanks for you help :D
You are welcome.
To find the number of bacteria after 3 hours, we need to determine the number of doubling periods within this time frame. First, we need to convert the 3 hours into minutes. Since there are 60 minutes in an hour, 3 hours is equal to 3 x 60 = 180 minutes.
Next, we can calculate the number of doubling periods by dividing the total time (in minutes) by the doubling period. In this case, the doubling period is 35 minutes.
So, the number of doubling periods is 180 / 35 = 5.14 (rounded to two decimal places).
Since we can't have a fractional number of bacteria, we need to take the closest whole number of doubling periods, which is 5.
To find the final number of bacteria, we can use the formula:
Final number of bacteria = Initial number of bacteria x (2 ^ number of doubling periods)
Here, the initial number of bacteria is 1400, and the number of doubling periods is 5.
Final number of bacteria = 1400 x (2 ^ 5) = 1400 x 32 = 44,800 bacteria.
Rounded to the nearest tenth, the final number of bacteria after 3 hours is approximately 44,800.