In 2004 a schools population was 1036 By 2008 the population

In 2004, a school\'s population was 1036. By 2008 the population had grown to 1764. Assume the population is changing linearly. How much did the population grow between the year 2004 and 2008? students How long did it take for the population to grow from 1036 students to 1764? years What is the average population growth per year? students per year What was the population in the year 2000? students Find an equation for the population, P, of the school t years after 2000. p(t) = Using your equation, predict the population of the school in 2011. students

Solution

(a) Increase in population = 1764 - 1036 = 728

(b) Required time = 2008-2004 = 4 years.

(c) avergare population growth per year = 728/4 =182 students/year.

(d) 2004 - 2000 = 4

So, population in 2000 is, 1036 - 4(182) = 308 students

(e) t = number of years sicne 2000

Then the linear equation for population after \"t\" years is,

y = mt + b, where

m = growth rate = 182 and

b= initial population (in 2000) = 308 (from part (d))

So, the equation is,

y = 182t + 308

(f) In 2011, t = 2011-2000 = 11

Sunstituting this in the above equation (from part (e)),

y = 182 (11)+308 = 2310 students