Question

A lawn mowing company is trying to grow it's buisness. It had 30 clans when it started its buisness and wants to increase by 6 new clients each week. Use ab arithmetic sequence to write a function to represent the real world situation and determine the range of the function for the first four weeks of data.

Answer 1

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 + 18; 0 ≤ y ≤ 4

Answer 2

The situation per week is 30 + 6n

where n is the number of weeks

Range of the function is 18 for the first four weeks of data

Explanation:

Here, we are to use an arithmetic sequence for a representation.

The first term here is a which is 30 clients while the common difference of d is 6 new clients per week

So we can write the nth term of the sequence as;

Tn = a + (n-1)d

Tn = 30 + (n-1)6

Tn = 30+ 6n -6

Tn = 24 + 6n

where n is the number of weeks

Now for the second week we shall have a total of a+ d clients = 30 + 6 = 36

For the third we have 24 + 6(3) = 24 + 18 = 42

For the fourth, we have 24 + 6(4) = 24 + 24 = 48

Thus the range mathematically means the difference between the highest and lowest for that four weeks = 48-30 = 18