Respuesta :
Answer:
(a) [tex]P_{t}=3(2)^{6t}[/tex]
(b) [tex]3(2)^{42}[/tex]
(c) 28.07 minutes
Step-by-step explanation:
A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.
That means sequence formed will be 3, 6, 12, 24............
We can easily say that this sequence is a geometric sequence having common ratio (r) = [tex]\frac{T_{2}}{T_{1}}=\frac{6}{3}[/tex]
r = 2
Now we know the explicit formula of a geometric sequence is given by
[tex]P_{t}=P_{0}(r)^{\frac{60t}{10}}=P_{0}(r)^{6t}[/tex]
Where a = Initial population = 3 bacteria
r = common ratio = 2
and t = time in hours
So explicit formula will be [tex]P_{t}=3(2)^{6t}[/tex]
(a) Now we have to calculate the size of population after t hours
[tex]P_{t}=3(2)^{6t}[/tex]
(b) We have to find the size of population after 7 hours or 420 minutes
[tex]P_{t}=3(2)^{6\times7}[/tex]
= [tex]3(2)^{42}[/tex]
After 7 hours bacteria population will be [tex]3(2)^{42}[/tex]
(c) Time to reach population as 21
By the explicit formula
[tex]21=3(2)^{6t}[/tex]
[tex]2^{6t}=\frac{21}{3}=7[/tex]
Now we take log on both the sides of the equation
[tex]log(2^{6t})=log(7)[/tex]
6t log2 = log 7
6t(0.301) = 0.845
t(1.806) = 0.845
t = [tex]\frac{0.845}{1.806}=0.468[/tex] hours
Or t = 0.468×60 = 28.07 minutes
Therefore, after 28.07 minutes bacterial population will be 21
The population after t hours is 3(2^6t).
The population after 7 hours is 3(2^42).
The population would be 21 in 19.45 minutes.
What is the function that represents the growth rate of the bacteria?
The formula that can be used to determine the population of the bacteria is:
The formula for calculating future value:
FV = P (1 + r)^n
Where:
- FV = Future value
- P = Present value = 3
- R = rate of growth = 100%
- N = time = (hours x 60 minutes) / 10 = 6t
Population in t hours = 3(2^6t)
Population in t hours = 3(2^42)
Time population would be 21 =[ (IN FV /PV) / r] X 10
(IN 21 / 3) / 1 = 19.45 minutes
To learn more about future value, please check: https://brainly.com/question/18760477
