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

Question

Mathematics

Frida Rocha

3 January, 02:25

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

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Natalee · Answer 1

f (x) = 3x + 26; 26 ≤ y ≤ 35

Step-by-step explanation:

This makes a linear equation.

y=mx+b

where m is the amount they want to increase each week

and b is the initial value i. e 26 clients.

Now substitute the values in the equation.

Let x=0

y=3 (0) + 26

y = 26

Now let x = 3

y=mx+b

y=3 (3) + 26

y=9+26

y=35

Thus the correct option is B.

f (x) = 3x + 26; 26 ≤ y ≤ 35 ...