Question

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.
$f( x) = 3x + 26;0 \leqslant y \leqslant 4$
B.
$f(x) = 3x + 26;26 \leqslant y \leqslant 35$
C.
$f(x) = 3x + 23;26 \leqslant y \leqslant 35$
D.
$f(x) = 3x + 23;0 \leqslant y \leqslant 4$


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Answer 1

Answer:

Option: B. is the correct answer.

  B.   $f(x)=3x+26\ ;\ 26\leq y\leq 35$

Step-by-step explanation:

It is given that:

A-mowing company is trying to grow its business. It had 26 clients when they started.

It had 26 clients when they started its business and wants to increase by 3 new clients each week.

i.e. if x represents the number of week, then the function which represents the number of clients is:

$f(x)=3x+26$

( Also, the range of the function is the set of all the values which are attained by a function in it's domain)

We are asked to find the range of the function for the first four weeks of data.

i.e. when x=0,1,2 and 3

i.e. x=0 is the initial week i.e. the first week when it was started.

x=1 is the second week after the start and so on.

Hence, we have:

the range as:   $26\leq y\leq 35$

Answer 2

Answer:

B. f(x) = 3x + 26;26≤ y ≤ 35

Step-by-step explanation:

This would be a linear equation in the form

y= mx+b

where b is the initial value (or 26 clients)

m is the slope, or the amount they want to increase by each week

y = 3x+26

Let x =0

y = 26 or what we start with

Let x =3, or be week 4 (we started with x= 0)

y = 3*3 +26

y =9+26

y= 35