Question

in 2001, a school population was 1467. by 2007 the population had grown to 1971. 1) how much did the population grow between the year 2001 and 2007? 2) how long did it take the population to grow from 1467 students to 1971 students? 3) what is the average population growth per year? 4) what was the population in the year 2000? 5) find an equation for the population, p, of the school t years after 2000. 6) using your equation, predict the population of the school in 2015. question help: video

Explanation:

Step1: Calculate population growth

Subtract the initial population from the final population. $1971 - 1467=504$.

Step2: Calculate time - interval

Subtract the initial year from the final year. $2007 - 2001 = 6$ years.

Step3: Calculate average population growth per year

Divide the total population growth by the number of years. $\frac{504}{6}=84$.

Step4: Find population in 2000

Assume linear growth. Since the population in 2001 was 1467 and the growth rate is 84 per year, the population in 2000 was $1467 - 84=1383$.

Step5: Find population equation

The general form of a linear equation is $P = P_0+rt$, where $P_0$ is the initial - population, $r$ is the rate of growth, and $t$ is the number of years. Here, $P_0 = 1383$ and $r = 84$, so $P=1383 + 84t$.

Step6: Predict population in 2015

The number of years from 2000 to 2015 is $t = 15$. Substitute $t = 15$ into the equation $P=1383+84\times15$. First, calculate $84\times15 = 1260$. Then, $P=1383 + 1260=2643$.

Answer:

1. 504 students
2. 6 years
3. 84
4. 1383 students
5. $P = 1383+84t$
6. 2643 students