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Answer:
ii cud givee uu an explanation for understandment for help if still don't understand im sowwyy thenn.
Step-by-step explanation:
It is given that the number of bacteria doubles every hour.
Therefore, the number of bacteria after every hour will form a G.P.
with first term (a=30) and common ratio (r=2)
∴a
3
=ar
2
=(30)(2)
2
=120
Therefore, the number of bacteria at the end of 2nd hour will be 480.
a
5
=ar
4
=(30)(2)
4
=480
and a
n+1
=ar
n
=(30)(2)
n
Thus the number of bacteria at the end of nth hour will be (30)(2)
n
Geometric sequence can model the considered situation. The number of bacteria in 18 hours for the considered situation will be 264
What is a geometric sequence and how to find its nth terms?
There are three parameters which differentiate between which geometric sequence we're talking about.
- The first parameter is the initial value of the sequence.
- The second parameter is the quantity by which we multiply previous term to get the next term.
- The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]d[/tex]
Then the sequence would look like
[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ad^{n-1}[/tex]
We can model the given situation with the geometric sequence since each previous count is being doubled(multiplied by 2) per 4 hours.
We're given initial number of bacteria = a = 22
Each new element will be denoting number of bacteria after 4 hours from previous count.
So, from 0 to 16 hours, there are four set of 4 hours. Thus, n = 4
Since number of bacteria are doubling, thus, d= 2
We get fourth term = number of bacteria after 16 hours
[tex]T_n = a(d)^{n-1} = 22 \times (2)^3 = 176[/tex]
Now, in the last 2 hours, assuming that if x -> 2x in 4 hours(which is increment of x), then in 2 hours, only x/2 must be incremented.(assuming linear growth in each 4 hour group).
Thus, after 18 hours, 176 + 176/2 will be the number of bacteria.
Thus, Number of bacteria after 18 hour for the given case = 176 + 88 = 264
Learn more about geometric sequence here:
https://brainly.com/question/2735005
