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A lawn-mowing company is trying to grow its business. it had 30 clients when they started its business and wants to increase by 6 new clients each week. use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data. f(x) = 6x 30; 0 ≤ y ≤ 4 f(x) = 6x 24; 0 ≤ y ≤ 4 f(x) = 6x 30; 30 ≤ y ≤ 48 f(x) = 6x 24; 30 ≤ y ≤ 48

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The function to represent the problem is f(x)=6x+24 and the range is 30[tex]\leq[/tex]y[tex]\leq[/tex]48.

What is arithmetic sequence formula?

If the terms of a sequence differ by a constant, we say the sequence is arithmetic. If the initial term ([tex]a_{0}[/tex]) of the sequence is a and the common difference is d, then we have,

[tex]a_{n}[/tex]=a+(n-1)d

Initial number of clients=30

Number increase per week= 6

So, we can make an arithmetic sequence fir six weeks

30,36,42,48

Here, first term, a=30

Common difference, d=6

Range is [30,48]

The explicit formula of an arithmetic sequence is

[tex]a_{n}[/tex]=a+(n-1)d

Put a=30, d=6, n=x

[tex]a_{x}[/tex]=30+(x-1)6

[tex]a_{x}[/tex]=30+6x-6

[tex]a_{x}[/tex]=6x+24

Therefore, The function to represent the problem is f(x)=6x+24 and the range is 30<=y<=48

To learn more about arithmetic sequence, visit: https://brainly.com/question/15412619

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