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Suppose a scientist reported the following data regarding the presence bacteria during the first four hours of testing for a new antibiotic:
90.000: 81,000; 72,900; 65,610
Model this sequence recursively
1
2. = 90,000(09)*-*
2
4; = 90,000,4, 0.9(a)
3.
a, 90.000- 9,000(1-1)
4
a = 90,000.0, -, -9,000
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Sagot :

The recursive geometric sequence that models this situation is:

[tex]f(n) = 0.9f(n-1)[/tex]

[tex]f(1) = 90000[/tex]

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

It can be represented by a recursive sequence as follows:

[tex]f(n) = qf(n-1)[/tex]

With f(1) as the first term.

In this problem, the sequence is: 90.000: 81,000; 72,900; 65,610, hence:

[tex]q = \frac{65610}{72900} = \cdots = \frac{81000}{90000} = 0.9[/tex]

[tex]f(1) = 90000[/tex]

Hence:

[tex]f(n) = 0.9f(n-1)[/tex]

[tex]f(1) = 90000[/tex]

More can be learned about geometric sequences at https://brainly.com/question/11847927

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