Chapter 3.5, Problem 23PPS

(a)

To determine

Write a function to represent Ryan`s commission.

Answer to Problem 23PPS

  $f(n)=0.80n$

Explanation of Solution

Given:

The points (10, 8), (20, 16), (30, 24), (40, 32), (50, 40), (60, 48) and (70, 56)

Concept Used:

Y − Coordinate of the points are the terms of the sequence.

The arithmetic sequence is $8,16,24,32,40,48,56\dots \dots \dots .$

Calculation:

The arithmetic sequence is $8,16,24,32,40,48,56\dots \dots \dots .$

  $a_1=8a_2=16a_3=24$

Find the common difference: $d=a_2-a_1=16-8=8\text{or}d=a_3-a_2=24-16=8$

The sequence is increasing, so the common difference is positive 8.

Write the equation for the nth term of arithmetic sequence with first term 8 and common difference 8.

  $a_1=8;d=8$

  $\begin{array}{l}{a}_n=a_1+(n-1)d\text{Formula}\text{for}\text{the}nth\text{term}\\ a_n=8+(n-1)·8a_1=8\text{and}d=8\\ a_n=8+8n-8\text{Distributive}\text{Property}\\ a_n=8n\text{Simplify}.\end{array}$

The difference of x coordinate is: $20-10=10$

Function: $f(n)=\frac{a_n}{\text{Difference}\text{of}\text{x}\text{cordinate}}=\frac{8n}{10}=0.8n$

So, the function for this arithmetic sequence is $f(n)=0.80n$

Thus, the function for this arithmetic sequence is $f(n)=0.80n$

(b)

To determine

Graph the function and determine the domain.

Answer to Problem 23PPS

The domain is {10, 20, 30, 40 …..}

Explanation of Solution

Given:

The points (10, 8), (20, 16), (30, 24), (40, 32), (50, 40), (60, 48) and (70, 56)

Concept Used:

Y − Coordinate of the points are the terms of the sequence.

The arithmetic sequence is $8,16,24,32,40,48,56\dots \dots \dots .$

Calculation:

The points to graph are represented by (n, f(n)) .

So, the points are (10, 8), (20, 16), (30, 24), (40, 32), (50, 40), (06, 48), (70, 56),

  

The domain of the function is the number of 10 − foot 2 x 4 planks cut.

So, the domain is {10, 20, 30, 40 …..}

Thus, the domain is {10, 20, 30, 40 …..}