# Alberta has a population growth rate of 3.1% per year. Its population in 2007 was approximately 3.5 million. a) Write an expression that predicts Alberta's population. b) Predict Alberta's...

Alberta has a population growth rate of 3.1% per year. Its population in 2007 was approximately 3.5 million.

a) Write an expression that predicts Alberta's population.

b) Predict Alberta's population in 2017 and in 2027 if the 2007 growth rate continues.

c) If the growth rate has been consistent, what was Alberta's population in 2000 and 1997.

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### 2 Answers

The rate of growth of Alberta's population is 3.1% per year. Therefore if the population in the base year is P, after n number of years the population will increase at a compounded rate and will be equal to P*(1 + .031) ^n or P*1.031^n.

As its population in 2007 is 3.5 million, in 2017 the population will be 3.5* 1.031^10 = 4.74 million and in 2027 it will be 3.5* 1.031^20 = 6.44 million.

If the rate of growth was the same, the population in the year 2000 was 3.5/1.031^7 = 2.82 million. In 1997 the population was 3.5/1.031^10 = 2.57 million.

The growth rate of the population of Alberta = r= 3.1%.

The population of Alberta in 2007 was P(2007) = 3.5 million.

a)

So the population of Alberta in 2017 = P(2007)*(1+r)^(20017-2007) = (3.5*10^6)(1.031)^(10) = 4.749574*10^6 = 4749574.

b)

In 2027 the population of Alberta at the rate of 3.1% growth will be P(2007)*(.031)^(2027-2007) = 3.5*10^6*(1.031)^20 = 6445273.

c)

The population of Alberta in 2000 and 1997 were as follows:

P(2000) = P(2007)*(1.031)^(2000-2007) = 3.5*(1.031)^(-7) million = 2826555

P(1997) = P(2007)*1.031^(1997-2007) = 3.5*1.031^(-10) = 2579178.