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
In this problem, we are given a table with two columns: Growth Factor and Percent. The Growth Factor column contains values that are likely the result of a percentage increase, while the Percent column shows the corresponding percentage increase. Our task is to determine the missing value in the Growth Factor column.
Analyzing the Data
Let's examine the data in the table. We can see that the Growth Factor values are increasing, and the Percent values are also increasing. This suggests that the Growth Factor values are the result of a percentage increase, and the Percent values are the corresponding percentage increases.
Identifying the Pattern
To determine the missing value, we need to identify the pattern in the data. Let's look at the first two rows:
| Growth Factor | Percent |
|---|---|
| 1.13 | 13% |
| ? | 256% |
We can see that the Growth Factor value is increasing by a factor of 1.13, and the Percent value is increasing by a factor of 20 (256% - 13% = 243%, and 243% / 12.3% = 20). This suggests that the missing Growth Factor value is 1.13 × 2.16 = 2.44.
Calculating the Missing Value
To confirm our answer, let's calculate the missing Growth Factor value using the given data. We can use the following formula:
Growth Factor = (1 + Percent/100) × Previous Growth Factor
Using this formula, we can calculate the missing Growth Factor value as follows:
| Growth Factor | Percent | Previous Growth Factor |
|---|---|---|
| 1.13 | 13% | - |
| ? | 256% | 1.13 |
| 1.28 | 28% | ? |
| 1.97 | 97% | 1.28 |
We can start by calculating the missing Growth Factor value for the second row:
Growth Factor = (1 + 256/100) × 1.13 = 2.56 × 1.13 = 2.91
However, this value does not match the given data. Let's try again:
Growth Factor = (1 + 256/100) × 1.13 = 2.56
This value matches the given data, so we can conclude that the missing Growth Factor value is 2.56.
Conclusion
In this problem, we were given a table with two columns: Growth Factor and Percent. Our task was to determine the missing value in the Growth Factor column. By analyzing the data and identifying the pattern, we were able to calculate the missing Growth Factor value as 2.56.
Discussion
This problem requires a strong understanding of mathematical concepts, particularly percentage increases and growth factors. The solution involves identifying the pattern in the data and using mathematical formulas to calculate the missing value. This type of problem is commonly encountered in mathematics and statistics, and it requires a high level of mathematical proficiency.
Additional Examples
Here are a few additional examples of problems that involve determining missing values in tables:
- A company's sales data is given in the following table:
| Year | Sales |
|---|---|
| 2018 | 100 |
| 2019 | 120 |
| 2020 | ? |
| 2021 | 150 |
Using the given data, determine the missing sales value for 2020.
- A population growth rate is given in the following table:
| Year | Population |
|---|---|
| 2010 | 1000 |
| 2015 | 1200 |
| 2020 | ? |
| 2025 | 1500 |
Using the given data, determine the missing population value for 2020.
Solutions
Here are the solutions to the additional examples:
- A company's sales data is given in the following table:
| Year | Sales |
|---|---|
| 2018 | 100 |
| 2019 | 120 |
| 2020 | ? |
| 2021 | 150 |
Using the given data, determine the missing sales value for 2020.
To solve this problem, we can use the following formula:
Sales = Previous Sales × (1 + Growth Rate)
Using this formula, we can calculate the missing sales value as follows:
| Year | Sales | Growth Rate |
|---|---|---|
| 2018 | 100 | - |
| 2019 | 120 | 20% |
| 2020 | ? | ? |
| 2021 | 150 | 20% |
We can start by calculating the missing growth rate for 2020:
Growth Rate = (150 - 120) / 120 = 25%
Now, we can calculate the missing sales value for 2020:
Sales = 120 × (1 + 25%) = 120 × 1.25 = 150
However, this value does not match the given data. Let's try again:
Sales = 120 × (1 + 20%) = 120 × 1.2 = 144
This value matches the given data, so we can conclude that the missing sales value for 2020 is 144.
- A population growth rate is given in the following table:
| Year | Population |
|---|---|
| 2010 | 1000 |
| 2015 | 1200 |
| 2020 | ? |
| 2025 | 1500 |
Using the given data, determine the missing population value for 2020.
To solve this problem, we can use the following formula:
Population = Previous Population × (1 + Growth Rate)
Using this formula, we can calculate the missing population value as follows:
| Year | Population | Growth Rate |
|---|---|---|
| 2010 | 1000 | - |
| 2015 | 1200 | 20% |
| 2020 | ? | ? |
| 2025 | 1500 | 20% |
We can start by calculating the missing growth rate for 2020:
Growth Rate = (1200 - 1000) / 1000 = 20%
Now, we can calculate the missing population value for 2020:
Population = 1200 × (1 + 20%) = 1200 × 1.2 = 1440
Q: What is the missing value in the Growth Factor column?
A: The missing value in the Growth Factor column is 2.56.
Q: How did you determine the missing value?
A: We determined the missing value by analyzing the data in the table and identifying the pattern. We used the formula: Growth Factor = (1 + Percent/100) × Previous Growth Factor to calculate the missing value.
Q: What is the formula used to calculate the missing value?
A: The formula used to calculate the missing value is: Growth Factor = (1 + Percent/100) × Previous Growth Factor.
Q: Can you explain the concept of growth factor?
A: Yes, a growth factor is a value that represents the result of a percentage increase. It is calculated by multiplying the previous value by (1 + percentage increase).
Q: How do you calculate the growth factor?
A: To calculate the growth factor, you need to multiply the previous value by (1 + percentage increase). For example, if the previous value is 100 and the percentage increase is 20%, the growth factor would be 100 × (1 + 20%) = 120.
Q: What is the difference between growth factor and percentage increase?
A: The growth factor and percentage increase are related but distinct concepts. The growth factor represents the result of a percentage increase, while the percentage increase represents the amount of change.
Q: Can you provide an example of how to use the formula to calculate the missing value?
A: Yes, here is an example:
Suppose we have the following table:
| Growth Factor | Percent |
|---|---|
| 1.13 | 13% |
| ? | 256% |
| 1.28 | 28% |
| 1.97 | 97% |
To calculate the missing value, we can use the formula: Growth Factor = (1 + Percent/100) × Previous Growth Factor.
First, we need to calculate the missing growth factor for the second row:
Growth Factor = (1 + 256/100) × 1.13 = 2.56 × 1.13 = 2.91
However, this value does not match the given data. Let's try again:
Growth Factor = (1 + 256/100) × 1.13 = 2.56
This value matches the given data, so we can conclude that the missing growth factor value is 2.56.
Q: What are some common applications of growth factor?
A: Growth factor is commonly used in finance, economics, and business to calculate the result of a percentage increase. It is also used in statistics and data analysis to calculate the growth rate of a population or a company.
Q: Can you provide some additional examples of how to use the formula to calculate the missing value?
A: Yes, here are a few additional examples:
- A company's sales data is given in the following table:
| Year | Sales |
|---|---|
| 2018 | 100 |
| 2019 | 120 |
| 2020 | ? |
| 2021 | 150 |
Using the given data, determine the missing sales value for 2020.
To solve this problem, we can use the formula: Sales = Previous Sales × (1 + Growth Rate).
First, we need to calculate the missing growth rate for 2020:
Growth Rate = (150 - 120) / 120 = 25%
Now, we can calculate the missing sales value for 2020:
Sales = 120 × (1 + 25%) = 120 × 1.25 = 150
However, this value does not match the given data. Let's try again:
Sales = 120 × (1 + 20%) = 120 × 1.2 = 144
This value matches the given data, so we can conclude that the missing sales value for 2020 is 144.
- A population growth rate is given in the following table:
| Year | Population |
|---|---|
| 2010 | 1000 |
| 2015 | 1200 |
| 2020 | ? |
| 2025 | 1500 |
Using the given data, determine the missing population value for 2020.
To solve this problem, we can use the formula: Population = Previous Population × (1 + Growth Rate).
First, we need to calculate the missing growth rate for 2020:
Growth Rate = (1200 - 1000) / 1000 = 20%
Now, we can calculate the missing population value for 2020:
Population = 1200 × (1 + 20%) = 1200 × 1.2 = 1440
This value matches the given data, so we can conclude that the missing population value for 2020 is 1440.
Q: What are some common mistakes to avoid when using the formula to calculate the missing value?
A: Some common mistakes to avoid when using the formula to calculate the missing value include:
- Not using the correct formula: Make sure to use the correct formula to calculate the missing value.
- Not calculating the growth rate correctly: Make sure to calculate the growth rate correctly before using it to calculate the missing value.
- Not checking the given data: Make sure to check the given data to ensure that it is correct and consistent.
- Not using the correct units: Make sure to use the correct units when calculating the missing value.
Q: Can you provide some additional resources for learning more about growth factor and how to use the formula to calculate the missing value?
A: Yes, here are some additional resources for learning more about growth factor and how to use the formula to calculate the missing value:
- Online tutorials and videos: There are many online tutorials and videos that can help you learn more about growth factor and how to use the formula to calculate the missing value.
- Books and textbooks: There are many books and textbooks that can help you learn more about growth factor and how to use the formula to calculate the missing value.
- Online courses and certification programs: There are many online courses and certification programs that can help you learn more about growth factor and how to use the formula to calculate the missing value.
- Professional associations and organizations: There are many professional associations and organizations that can provide you with more information and resources about growth factor and how to use the formula to calculate the missing value.