Question

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

Answer 1

The function to represent the problem is f(x)=6x+24 and the range is 30$\leq$y$\leq$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 ($a_{0}$) of the sequence is a and the common difference is d, then we have,

$a_{n}$=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

$a_{n}$=a+(n-1)d

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

$a_{x}$=30+(x-1)6

$a_{x}$=30+6x-6

$a_{x}$=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: brainly.com/question/15412619

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