Question

A lawn-mowing company is trying to grow its business. It had 18 clients when they started its business and wants to increase by 4 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.A.
`f( x) = 3x + 26;0 \leqslant y \leqslant 4`B.
`f(x) = 3x + 26;26 \leqslant y \leqslant 35`C.
`f(x) = 3x + 23;26 \leqslant y \leqslant 35`D.
`f(x) = 3x + 23;0 \leqslant y \leqslant 4`​

Answer 1

Are you sure those are the options to that description?

I did the test and the options were:

A) f(x) = 4x + 14; 0 ≤ y ≤ 4

B) f(x) = 4x + 18; 0 ≤ y ≤ 4

C) f(x) = 4x + 14; 18 ≤ y ≤ 30

D) f(x) = 4x + 18; 18 ≤ y ≤ 30

If those are the options, then the answer would be:

Answer:

D) f(x) = 4x + 18; 18 ≤ y ≤ 30

Explanation:

It would be that because if they want to increase by 4 customers every week you would attached that to x and since they started out with 18 customers they add 18 to the total weeks.

Answer 2

`f(x)=4x+14;18\le y\le 30`

Explanation:

Note: The given options are incorrect.

It is given that a company had 18 clients when they started its business and wants to increase by 4 new clients each week.

18, 22, 26, 30,...

First term of arithmetic sequence = 18

Common difference = 4

The explicit formula of an arithmetic sequence is

`a_n=a+(n-1)d`

where, a is first term and d is common difference.

Substitute a=18 and d=4 in the above formula.

`a_n=18+(n-1)4`

`a_n=18+4n-4`

`a_n=14+4n`

The function notation is

`f(x)=4x+14`

The number of clients in first four weeks are

18, 22, 26, 30

Therefore, the required function is
`f(x)=4x+14` and the range of the function for the first four weeks of data
`18\le y\le 30`.