A bacteria has a doubling period of 8 days. If there are 2900 bacteria present now, how many will there be in 20 days?
First we must find the daily growth rate (Round this to four decimal places).
The growth rate is
.
Then we use this rate to answer the question.
There will be
bacteria
step by step
"A bacteria has a doubling period of 8 days. If there are 2900 bacteria present now"
-----> count = 2900(2)^(t/8) , where t is number of days
replace t with 20 and start pushing buttons on your calculator
the daily growth factor is 2^(1/8) = 1.0905
That means a daily growth rate of 9.05%
To find the daily growth rate of the bacteria, we can use the formula:
Growth rate = 1 / Doubling period
In this case, the doubling period is 8 days. So, the growth rate is:
Growth rate = 1 / 8 = 0.125
Now, let's use this growth rate to calculate the number of bacteria after 20 days.
To find the number of bacteria after a certain period of time, we can use the formula:
Final number of bacteria = Initial number of bacteria * (1 + Growth rate)^Number of periods
In this case, the initial number of bacteria is 2900, the growth rate is 0.125, and the number of periods is 20.
Using the formula, we can substitute the values:
Final number of bacteria = 2900 * (1 + 0.125)^20
Calculating this expression, we find:
Final number of bacteria ≈ 21,574.56
Therefore, after 20 days, there will be approximately 21,575 bacteria.