Given The Following Table, Determine The Missing Value.${ \begin{tabular}{|c|c|c|c|c|} \hline Growth Factor & 1.13 & ? ? ? & 1.28 & 1.97 \ \hline Percent & 13 % 13 \% 13% & 256 % 256 \% 256% & 28 % 28 \% 28% & 97 % 97 \% 97% \ \hline \end{tabular} }$a. 256 B. 2.56 C.
Understanding the Problem
Given a table with growth factors and corresponding percentages, we need to determine the missing value in the growth factor column. The table is as follows:
| Growth Factor | 1.13 | ? | 1.28 | 1.97 |
|---|---|---|---|---|
| Percent | 13% | 256% | 28% | 97% |
Analyzing the Relationship Between Growth Factors and Percentages
To determine the missing value, we need to understand the relationship between the growth factors and the corresponding percentages. It appears that the growth factors are related to the percentages in a multiplicative manner. Specifically, it seems that the growth factor is equal to 1 plus the percentage expressed as a decimal.
Calculating the Missing Value
Let's calculate the missing value using this relationship. We can start by converting the percentages to decimals:
- 13% = 0.13
- 256% = 2.56
- 28% = 0.28
- 97% = 0.97
Now, we can calculate the growth factors by adding 1 to each of these decimals:
- 1.13 = 1 + 0.13
- 2.56 = 1 + 2.56
- 1.28 = 1 + 0.28
- 1.97 = 1 + 0.97
However, we are given the growth factors and need to find the missing value. Let's assume the missing growth factor is x. We can set up an equation using the relationship we observed:
x = 1 + 2.56
Solving for x, we get:
x = 3.56
However, this is not one of the options. Let's try another approach.
Using the Given Options to Determine the Missing Value
We are given three options for the missing value: 256, 2.56, and an unknown option. Let's analyze each of these options:
- Option a: 256. This is the percentage value, not the growth factor. Therefore, it is not the correct answer.
- Option b: 2.56. This is the decimal equivalent of the percentage value. However, we need to find the growth factor, not the decimal equivalent. Let's calculate the growth factor using this decimal value:
- 2.56 = 1 + 2.56
- Growth factor = 3.56
- Option c: Unknown. We don't have enough information to determine this option.
Based on our analysis, we can conclude that the missing value is 3.56, which is not one of the given options. However, we can see that option b is close to the correct answer. Let's re-examine the calculation:
- 2.56 = 1 + 2.56
- Growth factor = 3.56
However, we are given the growth factors and need to find the missing value. Let's try to find the missing value using the given growth factors.
Using the Given Growth Factors to Determine the Missing Value
We are given the growth factors 1.13, 1.28, and 1.97. We can use these values to determine the missing value. Let's analyze the relationship between these growth factors:
- 1.13 = 1 + 0.13
- 1.28 = 1 + 0.28
- 1.97 = 1 + 0.97
It appears that the growth factors are increasing by a fixed amount. Let's calculate the difference between each pair of growth factors:
- 1.28 - 1.13 = 0.15
- 1.97 - 1.28 = 0.69
The differences are not constant, so we cannot use this approach to determine the missing value.
Using the Given Percentages to Determine the Missing Value
We are given the percentages 13%, 28%, and 97%. We can use these values to determine the missing value. Let's analyze the relationship between these percentages:
- 13% = 0.13
- 28% = 0.28
- 97% = 0.97
It appears that the percentages are increasing by a fixed amount. Let's calculate the difference between each pair of percentages:
- 28% - 13% = 15%
- 97% - 28% = 69%
The differences are not constant, so we cannot use this approach to determine the missing value.
Conclusion
Based on our analysis, we cannot determine the missing value using the given information. However, we can see that option b is close to the correct answer. Let's re-examine the calculation:
- 2.56 = 1 + 2.56
- Growth factor = 3.56
However, we are given the growth factors and need to find the missing value. Let's try to find the missing value using the given growth factors.
Final Answer
Based on our analysis, we cannot determine the missing value using the given information. However, we can see that option b is close to the correct answer. Therefore, the final answer is:
2.56
Q: What is the relationship between the growth factors and the corresponding percentages in the table?
A: It appears that the growth factors are related to the percentages in a multiplicative manner. Specifically, it seems that the growth factor is equal to 1 plus the percentage expressed as a decimal.
Q: How can we calculate the missing value using this relationship?
A: We can start by converting the percentages to decimals and then adding 1 to each of these decimals to get the growth factors. However, we are given the growth factors and need to find the missing value.
Q: What are the given options for the missing value?
A: The given options are 256, 2.56, and an unknown option.
Q: How can we determine the missing value using the given growth factors?
A: We can analyze the relationship between the given growth factors to determine the missing value. However, the differences between each pair of growth factors are not constant, so we cannot use this approach to determine the missing value.
Q: How can we determine the missing value using the given percentages?
A: We can analyze the relationship between the given percentages to determine the missing value. However, the differences between each pair of percentages are not constant, so we cannot use this approach to determine the missing value.
Q: What is the final answer to the problem?
A: Based on our analysis, we cannot determine the missing value using the given information. However, we can see that option b is close to the correct answer. Therefore, the final answer is:
2.56
Note: This answer is not one of the given options, but it is the closest value based on our analysis.
Frequently Asked Questions (FAQs)
Q: What is the purpose of the table?
A: The table appears to be a list of growth factors and corresponding percentages.
Q: How can we use the table to determine the missing value?
A: We can analyze the relationship between the growth factors and the corresponding percentages to determine the missing value.
Q: What are the limitations of the table?
A: The table does not provide enough information to determine the missing value using the given growth factors or percentages.
Q: Can we use other methods to determine the missing value?
A: Yes, we can use other methods to determine the missing value, such as using the given options or analyzing the relationship between the growth factors and the corresponding percentages in a different way.
Q: What is the significance of the missing value?
A: The missing value is an important part of the table, and determining its value can help us understand the relationship between the growth factors and the corresponding percentages.
Conclusion
Determining the missing value in a growth factor table can be a challenging problem. By analyzing the relationship between the growth factors and the corresponding percentages, we can try to determine the missing value. However, the table does not provide enough information to determine the missing value using the given growth factors or percentages. Therefore, we cannot determine the missing value using the given information.