# According to the 1991 census, the region of Niagara, Ontario, had 364552 residents. For the next few years, the population grew at a rate of 2.2% ...per year. For planning purposes, the regional...

According to the 1991 census, the region of Niagara, Ontario, had 364552 residents. For the next few years, the population grew at a rate of 2.2% ...

per year. For planning purposes, the regional government needs to determine the population of the region in 2010. The algebraic model for this case is P(n)=P(0)*(1+r)^n

A) What is the initial population, Po ?

b) What is the growth rate, r?

c) How many growth periods, n, are there?

d) Write the algebraic model for this situation.

e) Use the model to determine the population in 2010.

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### 1 Answer

The initial population in the year 1991 is given as 364552.

The rate of growth is also given as 2.2%.

The number of growth periods is not limited by any factor as the population is not decreasing but increasing. Between the years 2010 and 1991 though the number of growth periods is 2010 - 1991 = 19

The algebraic model of the population is given as 364552*(1.022)^n.

This can be used to determine the population in 2010; n is equal to 2010 - 1991 = 19, which gives the population in year 2010 as 364552*(1.022)^19 = 551221.