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 + 24; 30 ≤ y ≤ 54

f (x) = 6x + 30; 30 ≤ y ≤ 54

So, f (x) = 6 x + 30; 0 ≤ y ≤ 4

Step-by-step explanation:

Given: A lawn-mowing company had 30 clients when they started its business and wants to increase by 6 new clients each week.

To find: arithmetic sequence to write a function to represent the real-world situation and the range of the function for the first four weeks of data.

Solution:

A sequence is a list of numbers in a specific order following some pattern.

A sequence is said to be arithmetic if difference between the terms is same.

For the first week, number of clients = 30

For the second week, number of clients = 30 + 6 (1)

For the third week, number of clients = 30 + 6 (2)

For the third week, number of clients = 30 + 6 (3)

For the fourth week, number of clients = 30 + 6 (4)

So, f (x) = 6 x + 30; 0 ≤ y ≤ 4