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.
Of(x)=6x +30,0 ≤ y ≤4
Of(x)=6x+24; 0 < y < 4
Of(x)=6x +30, 30 ≤ y ≤ 48
Of(x)=6x+24; 30 ≤ y ≤ 48

Answer 1

Explanation:

Option C.

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

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

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

The function notation is

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

Therefore, the correct option is C.