Question content area top

Question

Part 1
The table shows the number of cell phone towers a company will build as the number of its customers increases. Complete a and b below.
Cell Phone Towers
Customers​ (thousands)
Towers
4.25
204
5.25
252
6.25
300
8.25
396
Question content area bottom
Part 1
a. Is the relationship between number of towers and number of customers​ proportional? Explain. Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
No. The ratios of towers to customers are not all equivalent.
B.
Yes. The ratios of towers to customers​ (thousands) are all equivalent to a unit rate of
  
enter your response here.

Answer 1

To determine if the relationship between the number of cell phone towers and the number of customers is proportional, we need to calculate the ratio of the number of towers to the number of customers for each given data point and see if these ratios are equivalent.

Here are the calculations for each data point:

1. For 4.25 thousand customers:
   \(\frac{204 \text{ towers}}{4.25 \text{ thousands customers}} = \frac{204}{4.25} = 48\) towers per thousand customers.

2. For 5.25 thousand customers:
   \(\frac{252 \text{ towers}}{5.25 \text{ thousands customers}} = \frac{252}{5.25} = 48\) towers per thousand customers.

3. For 6.25 thousand customers:
   \(\frac{300 \text{ towers}}{6.25 \text{ thousands customers}} = \frac{300}{6.25} = 48\) towers per thousand customers.

4. For 8.25 thousand customers:
   \(\frac{396 \text{ towers}}{8.25 \text{ thousands customers}} = \frac{396}{8.25} = 48\) towers per thousand customers.

Since all calculated ratios are equal to 48, we can conclude that:

A. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of 48.