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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
238
5.25
294
6.25
350
8.25
462
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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 whether the relationship between the number of towers and the number of customers is proportional, we need to check the ratio of towers to customers for each pair of values and see if they are equivalent.

Given data (Customers in thousands and Towers):

1. For 4.25 thousand customers:
   \[ \text{Ratio} = \frac{238 \text{ towers}}{4.25 \text{ thousand customers}} = \frac{238}{4.25} \approx 55.88 \]

2. For 5.25 thousand customers:
   \[ \text{Ratio} = \frac{294 \text{ towers}}{5.25 \text{ thousand customers}} = \frac{294}{5.25} \approx 56.00 \]

3. For 6.25 thousand customers:
   \[ \text{Ratio} = \frac{350 \text{ towers}}{6.25 \text{ thousand customers}} = \frac{350}{6.25} \approx 56.00 \]

4. For 8.25 thousand customers:
   \[ \text{Ratio} = \frac{462 \text{ towers}}{8.25 \text{ thousand customers}} = \frac{462}{8.25} \approx 56.00 \]

Now, let's review these ratios:

• The ratio for 4.25 thousand customers is approximately 55.88.
• The ratios for 5.25, 6.25, and 8.25 thousand customers are all approximately 56.00.

Since the ratios are not all equivalent (the first one is approximately 55.88, while the others are approximately 56.00), the relationship is not proportional.

The correct choice is:

A. No. The ratios of towers to customers are not all equivalent.