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Intro to Linear Models

Question 1:

In 2010, the number of clown costumes sold at a single costume shop was 12. By 2015, that number had grown to 42. Assuming a constant increase in clown costume sales, calculate the average rate of change (the slope) from 2010 to 2015. Round your answer to the nearest tenth.



Answer :

GinnyAnswer
To solve this problem, we need to calculate the average rate of change (or the slope) in the number of clown costumes sold from 2010 to 2015. Here’s a step-by-step guide to finding the solution:

1. Identify the given data:
- Number of clown costumes sold in 2010: 12
- Number of clown costumes sold in 2015: 42
- Year 2010: 2010
- Year 2015: 2015

2. Calculate the change in the number of clown costumes sold:
[tex]\[ \text{Change in costumes} = \text{Number of costumes in 2015} - \text{Number of costumes in 2010} \][/tex]
[tex]\[ \text{Change in costumes} = 42 - 12 = 30 \][/tex]

3. Calculate the change in time (in years):
[tex]\[ \text{Change in time} = \text{Year 2015} - \text{Year 2010} \][/tex]
[tex]\[ \text{Change in time} = 2015 - 2010 = 5 \][/tex]

4. Calculate the average rate of change (or the slope):
[tex]\[ \text{Average rate of change} = \frac{\text{Change in costumes}}{\text{Change in time}} \][/tex]
[tex]\[ \text{Average rate of change} = \frac{30}{5} = 6.0 \][/tex]

5. Round the average rate of change to the nearest tenth:
Since the value is 6.0, it is already rounded to the nearest tenth.

Therefore, the average rate of change in the number of clown costumes sold from 2010 to 2015, rounded to the nearest tenth, is 6.0 costumes per year.

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