Question
In 2001, a school population was 2224. By 2008 the population had grown to 2903.
1) How much did the population grow between the year 2001 and 2008?
students
2) How long did it take the population to grow from 2224 students to 2903 students?
years
3) What is the average population growth per year?
student
years
students/year
years/students
4) What was the population in the year 2000?
students
5) Find an equation for the population, P, t of the school
years after 2000.
P =
6) Using your equation, predict the population of the school in 2015.
students
1) How much did the population grow between the year 2001 and 2008?
students
2) How long did it take the population to grow from 2224 students to 2903 students?
years
3) What is the average population growth per year?
student
years
students/year
years/students
4) What was the population in the year 2000?
students
5) Find an equation for the population, P, t of the school
years after 2000.
P =
6) Using your equation, predict the population of the school in 2015.
students
Answers
Answered by
GPT-4o mini
Let's go through the steps one by one.
### 1) How much did the population grow between the year 2001 and 2008?
**Population growth = Population in 2008 - Population in 2001**
= 2903 - 2224 = **679 students.**
### 2) How long did it take the population to grow from 2224 students to 2903 students?
**Time taken = 2008 - 2001 = 7 years.**
### 3) What is the average population growth per year?
**Average growth per year = Total growth / Number of years**
= 679 students / 7 years ≈ **96.71 students/year.**
### 4) What was the population in the year 2000?
Assuming linear growth, we can find the population in 2000 by calculating backwards from 2001 (the population in 2001 is 2224).
**Population in 2000 = Population in 2001 - Average growth per year**
= 2224 - 96.71 ≈ **2127 students.**
### 5) Find an equation for the population, P, t of the school years after 2000.
The general form for a linear equation is \( P = P_0 + r \cdot t \), where:
- \( P_0 \) is the initial population (population in the year 2000),
- \( r \) is the average growth rate,
- \( t \) is the number of years after 2000.
Using the calculated numbers:
- \( P_0 = 2127 \),
- \( r ≈ 96.71 \).
So, the equation becomes:
\[ P = 2127 + 96.71t \]
### 6) Using your equation, predict the population of the school in 2015.
To find the population in 2015, we need to substitute \( t \) with \( 15 \) (since 2015 is 15 years after 2000):
\[ P = 2127 + 96.71 \cdot 15 \]
\[ P ≈ 2127 + 1450.65 \]
\[ P ≈ 3577.65 \]
Rounding, we can predict that the population in 2015 will be approximately **3578 students.**
### Summary of answers:
1. 679 students
2. 7 years
3. 96.71 students/year
4. 2127 students
5. \( P = 2127 + 96.71t \)
6. Approximately 3578 students
### 1) How much did the population grow between the year 2001 and 2008?
**Population growth = Population in 2008 - Population in 2001**
= 2903 - 2224 = **679 students.**
### 2) How long did it take the population to grow from 2224 students to 2903 students?
**Time taken = 2008 - 2001 = 7 years.**
### 3) What is the average population growth per year?
**Average growth per year = Total growth / Number of years**
= 679 students / 7 years ≈ **96.71 students/year.**
### 4) What was the population in the year 2000?
Assuming linear growth, we can find the population in 2000 by calculating backwards from 2001 (the population in 2001 is 2224).
**Population in 2000 = Population in 2001 - Average growth per year**
= 2224 - 96.71 ≈ **2127 students.**
### 5) Find an equation for the population, P, t of the school years after 2000.
The general form for a linear equation is \( P = P_0 + r \cdot t \), where:
- \( P_0 \) is the initial population (population in the year 2000),
- \( r \) is the average growth rate,
- \( t \) is the number of years after 2000.
Using the calculated numbers:
- \( P_0 = 2127 \),
- \( r ≈ 96.71 \).
So, the equation becomes:
\[ P = 2127 + 96.71t \]
### 6) Using your equation, predict the population of the school in 2015.
To find the population in 2015, we need to substitute \( t \) with \( 15 \) (since 2015 is 15 years after 2000):
\[ P = 2127 + 96.71 \cdot 15 \]
\[ P ≈ 2127 + 1450.65 \]
\[ P ≈ 3577.65 \]
Rounding, we can predict that the population in 2015 will be approximately **3578 students.**
### Summary of answers:
1. 679 students
2. 7 years
3. 96.71 students/year
4. 2127 students
5. \( P = 2127 + 96.71t \)
6. Approximately 3578 students