Sure, let's analyze the problem step-by-step.
### 1) Highlight/underline the knowns in this problem
In this problem, the known values provided are:
- Year 1: Number of applications received = 12300
- Year 2: Number of applications received = 12669
We can underline these known values in our given data table:
[tex]\[
\begin{array}{c|c}
\hline \text{Year, } n & \text{Number of applications received} \\
\hline
\underline{1} & \underline{12300} \\
\hline
\underline{2} & \underline{12669} \\
\hline
\end{array}
\][/tex]
### 2) Write down any unknowns in this problem
The unknowns in this problem are:
- The growth rate of applications per year.
- The number of applications in year 3 (or any subsequent year).
### Step-by-Step Solution
Let's break down the steps to find the unknowns:
Step 1: Determine the Growth Rate
We can assume a linear increase in the number of applications. In a linear growth model, the difference in the number of applications received each year remains constant.
The growth rate can be calculated as follows:
[tex]\[
\text{Growth Rate} = \frac{\text{Applications in Year 2} - \text{Applications in Year 1}}{\text{Year 2} - \text{Year 1}}
\][/tex]
Using the provided data:
[tex]\[
\text{Growth Rate} = \frac{12669 - 12300}{2 - 1} = \frac{369}{1} = 369
\][/tex]
So, the growth rate is 369 applications per year.
Step 2: Predict the Number of Applications in Year 3
To predict the number of applications in the third year, we add the growth rate to the number of applications in the second year:
[tex]\[
\text{Applications in Year 3} = \text{Applications in Year 2} + \text{Growth Rate}
\][/tex]
Using the provided data:
[tex]\[
\text{Applications in Year 3} = 12669 + 369 = 13038
\][/tex]
### Summary
- The known values are:
- Year 1: 12300 applications
- Year 2: 12669 applications
- The unknowns are:
- Growth rate: 369 applications/year
- Number of applications in Year 3: 13038 applications
