Question

in 2005, a school population was 899. by 2006 the population had grown to 1063. 1) how much did the population grow between the year 2005 and 2006? students 2) how long did it take the population to grow from 899 students to 1063 students? years 3) what is the average population growth per year? select an answer 4) what was the population in the year 2000? students 5) find an equation for the population, p, of the school t years after 2000. p = 6) using your equation, predict the population of the school in 2011. students

Explanation:

Step1: Calculate population growth from 2005 - 2006

$1063 - 899=164$

Step2: Determine time taken for growth

$2006 - 2005 = 1$

Step3: Calculate average population growth per year

$\frac{1063 - 899}{2006 - 2005}=\frac{164}{1}=164$

Step4: Assume linear growth, find population in 2000

Let the population growth be linear with the equation $P=mt + b$, where $m$ is the slope (average growth rate) and $t$ is the number of years after 2000. In 2005 ($t = 5$), $P = 899$. We know $m = 164$. Substitute into the equation: $899=164\times5 + b$. Then $b=899 - 820=79$

Step5: Write the population - time equation

$P = 164t+79$

Step6: Predict population in 2011

In 2011, $t = 11$. Substitute $t = 11$ into the equation $P=164\times11 + 79=1804 + 79=1883$

Answer:

1. 164
2. 1
3. 164
4. 79
5. $P = 164t+79$
6. 1883