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. f(x) = 4x + 14; 0 ≤ y ≤ 4 f(x) = 4x + 18; 0 ≤ y ≤ 4 f(x) = 4x + 14; 18 ≤ y ≤ 30 f(x) = 4x + 18; 18 ≤ y ≤ 30

Answer 1

Answer:

Option C.

Step-by-step explanation:

Initial number of clients = 18

Number of Increase per week = 4

We need to use an arithmetic sequence to write a function.

So, the required arithmetic sequence for four weeks is

18, 22, 26, 30

Here, first term is 18 and common difference is 4. The range is  [18,30].

The explicit formula of n 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.

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

$a_n=18+4n-4$

$a_n=4n+14$

The function notation is

$f(x)=4x+14$

The function is f(x)=4x+14 and the range is  18 ≤ y ≤ 30.

Therefore, the correct option is C.

Answer 2

Answer:

f(x) = 4x + 18; 18 ≤ y ≤ 30

Step-by-step 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.