   SEARCH HOME Math Central Quandaries & Queries  Question from Shelby, a student: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of -25,195 per year with t represents the number of years since 1994? Hi Shelby,

I am not sure what you want since I don't know if 547,725 is the population now or in 1947. Is the growth rate really negative? Is the city loosing 25,195 people every year? I'm going to do something similar that I hope will help.

Suppose that the population of a city is 453,256 in 2008 and the population has been growing by 12, 345 each year since the year 2000. Write a linear model to represent the population since 2000 using the variable t, the number of years since 2000.

It is 8 years since 2000 so the population is 2000 was 453,725 - 8 × 12,345 = 354,965. If t is the number of years since 2000 then the population in the year 2000 + t is

P(t) = 345,965 + t × 12,345.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.