A model for the population of a Canadian city

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Question from jess, a student:

Let t^2 represent t-squared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000?

Hi Jess,

If t = 0 is 2007 then t = 1 is 2008, t = 2 is 2009 and t = 3 is 2010. Thus in your expression

f(t) = 12t² + 800t + 40,000

substitute t = 3 to obtain the population that the model predicts for 2010.

For part b) you want t when 12t² + 800t + 40,000 = 300,000. You will need to use the quadratic formula to solve for t.

Penny

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