Question

1. company a quantity price 8 10 12 18 16 26 20 34 company b quantity price 3 5 6 20 9 35 12 50 a. what is the rate of change for company a? b. what is the rate of change for company b? c. which company offers budget - friendly prices for the customers? explain.

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate rate of change for Company A

Let's take two points from Company A's table, say $(8,10)$ and $(12,18)$. Then $m_A=\frac{18 - 10}{12 - 8}=\frac{8}{4}=2$.

Step3: Calculate rate of change for Company B

Take two points from Company B's table, say $(3,5)$ and $(6,20)$. Then $m_B=\frac{20 - 5}{6 - 3}=\frac{15}{3}=5$.

Step4: Compare and conclude

Since $2<5$, Company A has a lower rate of change in price with respect to quantity, so it is more budget - friendly.

Answer:

a. 2
b. 5
c. Company A. The rate of change (slope) for Company A is 2, while for Company B it is 5. A lower rate of change for Company A means that the price increases at a slower rate with an increase in quantity, making it more budget - friendly.