Question

assessment practice

1. the table shows the number of cell phone towers a company will build as the number of its customers increases.

part a
is the relationship between number of towers and number of customers proportional? explain. 7.ar.1
part b
if there are 576 towers, how many customers does the company have? write a proportion you can use to solve. 7.ar.3.2

Explanation:

Step1: Calculate the ratio for each pair

For the first pair: $\frac{252}{5.25}=\frac{252\times100}{5.25\times100}=\frac{25200}{525} = 48$
For the second pair: $\frac{300}{6.25}=\frac{300\times100}{6.25\times100}=\frac{30000}{625}=48$
For the third pair: $\frac{348}{7.25}=\frac{348\times100}{7.25\times100}=\frac{34800}{725}=48$
For the fourth pair: $\frac{444}{9.25}=\frac{444\times100}{9.25\times100}=\frac{44400}{925}=48$

Step2: Check the proportionality

Since the ratio $\frac{\text{Towers}}{\text{Customers (thousands)}}$ is constant ($k = 48$) for all pairs of values in the table.

Answer:

Part A: The relationship between the number of towers and the number of customers is proportional. Because the ratio of the number of towers to the number of customers (in thousands) is constant ($48$) for all data - pairs in the table.

Part B: Let $x$ be the number of customers (in thousands) when there are $576$ towers. The proportion is $\frac{576}{x}=\frac{252}{5.25}$ (or any other valid pair - based proportion, since $\frac{\text{Towers}}{\text{Customers (thousands)}}=48$, we can also write $\frac{576}{x}=48$)