The unemployment rates for Canada for selected years from 1970 to 2008 can be modeled by y=-0.009x^2 + 0.321x + 5.676 where x is the number of years after 1970

Step-by-step explanation:

Given the unemployment rates for Canada for selected years from 1970 to 2008 modeled by y=-0.009x² + 0.321x + 5.676 where x is the number of years after 1970, we are to find the following

a) The value of x that corresponds to the years 1990 to 2005. To get this we will take the difference between both years 1990 and 2005 i.e 2005 - 1990

x = 2005 - 1990

x = 15

Hence, the value of x that corresponds to the years 1990 to 2005 is 15 years since x is measured in years.

b) Find the value of y when x = 25. To get thos, we will substitute x = 25 into the modelled function to get y where y is the unemployment rate.

Given the function y=-0.009x² + 0.321x + 5.676

y = -0.009(25)² + 0.321(25) + 5.676

y = -5.625 + 8.025 + 5.676

y = 8.076

This means that the unemployment rates for Canada for selected years from 1970 to 1995 is 8.076% (note that the year difference between 1995 and 1970 is equivalent to 25)

c) To determine the unemployment rate in 2008, first we need to get the amount of years between 1970 and 2008.

The amount of years between 1970 and 2008 is expressed as x = 2008-1970

x = 38

Then substitute x = 38 into the modeled function as shown;

y = -0.009(38)² + 0.321(38) + 5.676

y = -12.996+12.198+5.676

y = 4.878

Hence, the the unemployment rate in 2008 is 4.878%