Answered

Find the best solutions to your problems with the help of IDNLearn.com. Get comprehensive and trustworthy answers to all your questions from our knowledgeable community members.

Activity 7

The admissions team at a new university is trying to predict the number of student applications they will receive each year.

Let [tex]$n$[/tex] be the number of years that the university has been open. The admissions team collected the following data for the first two years.

[tex]\[
\begin{tabular}{c|c}
\hline Year, $n$ & Number of applications received \\
\hline 1 & 12300 \\
\hline 2 & 12669 \\
\hline
\end{tabular}
\][/tex]

1. Highlight/underline the knowns in this problem.
2. Write down any unknowns in this problem.

Sagot :

GinnyAnsweridn
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
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.