A Bacteria has a doubling period of 8 days. If there are 2250 bacteria present now, how many will there be in 33 days?
find the growth rate (Round this to 4 decimal places).
Growth Rate___________.
There will be _________ Bacteria.
To find the growth rate, we use the formula N = N0 * (1 + r)^t, where N is the final population, N0 is the initial population, r is the growth rate, and t is time.
We know the initial population (N0) is 2250, and the doubling period means the population doubles every 8 days. We can use this information to find the growth rate.
Since the population doubles in 8 days, we have:
N = 2250 * 2 = 4500
Now we can plug this into the formula:
4500 = 2250 * (1 + r)^8
Now, we can solve for r:
(4500/2250) = (1 + r)^8
2 = (1 + r)^8
To isolate r, take the 8th root of both sides:
(2)^(1/8) = 1 + r
Now, subtract 1 from both sides:
(2)^(1/8) - 1 = r
Calculate:
r ≈ 0.0902
So the growth rate is approximately 0.0902 (rounded to 4 decimal places).
Now, we can use this growth rate to find the bacteria population in 33 days. We know the initial population is 2250, the growth rate is 0.0902, and t = 33.
Plug these values into the formula:
N = 2250 * (1 + 0.0902)^33
Calculate:
N ≈ 32891.46
Since we can't have a fraction of a bacteria, we round to the nearest whole number:
N ≈ 32891
So, there will be approximately 32,891 bacteria in 33 days.
Growth Rate: 0.0902
There will be 32,891 bacteria.
To find the growth rate, we can use the formula:
\(Growth\ Rate = \left(2^{\frac{1}{Doubling\ Period}}\right) - 1\)
Given that the doubling period is 8 days, we can substitute this value into the formula:
\(Growth\ Rate = \left(2^{\frac{1}{8}}\right) - 1\)
Using a calculator, we can evaluate this expression:
\(Growth\ Rate = 0.0907\)
Therefore, the growth rate is approximately 0.0907 (rounded to 4 decimal places).
To calculate the number of bacteria after 33 days, we can use the formula:
\(Final\ Population = Initial\ Population \times (1 + Growth\ Rate)^{\frac{Time}{Doubling\ Period}}\)
Substituting the given values, we have:
\(Final\ Population = 2250 \times (1 + 0.0907)^{\frac{33}{8}}\)
Using a calculator, we can evaluate this expression:
\(Final\ Population = 2250 \times (1.0907)^{4.125}\)
\(Final\ Population \approx 2250 \times 1.4000\)
\(Final\ Population \approx 3150\)
Therefore, there will be approximately 3150 bacteria after 33 days.
To find the growth rate, we need to use the formula:
Growth Rate = 2^(1/period) - 1
In this case, the doubling period is 8 days. Plugging the value into the formula:
Growth Rate = 2^(1/8) - 1
Using a calculator, we can evaluate this expression:
Growth Rate ≈ 0.0902
Now, to determine the number of bacteria after 33 days, we can use the formula:
Number of Bacteria = Initial Number of Bacteria * (1 + Growth Rate)^(time/period)
Plugging in the given values:
Initial Number of Bacteria = 2250
Growth Rate = 0.0902
Time = 33 days
Doubling Period = 8 days
Number of Bacteria = 2250 * (1 + 0.0902)^(33/8)
Again, using a calculator to evaluate this expression:
Number of Bacteria ≈ 15,352.76
Therefore:
Growth Rate ≈ 0.0902
There will be approximately 15,352.76 bacteria.