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1.) The population of city A is represented by PA = 4 + 0.5t and the population of city B is represented by PB = 1.5 + 0.9t. Consider that both equations express population in millions of people. Variable t represents number of years after year 2000.
a) By using only one Cartesian plane, sketch the graphs of both functions. Be accurate. Use either graph paper and ruler or copy and paste graph obtained by using a graphing calculator online. On your graph, estimate the coordinates of the point of intersection.
b) Algebraically, find the value of t when both cities have the same population. Hint: When both populations are equal, we can state that PA = PB.
c) What is that population?
2.) A floor refinishing company charges $5.25 per square foot to strip and refinish a tile floor for up to 800 square feet. There is an additional charge of $480 for toxic waste disposal for any job that includes more than 200 square feet of tile.
a) Express the cost, y, of refinishing a floor as function of the number of square feet, x, to be refinished.
b) Sketch the function.
c) What are the domain and range of the function.
3.) Function f ( x) = 3( x − 5)2 + 9 is transformed as follows.
a) f(x)is shifted 6 units to right to obtain function g(x). What is the equation of g(x) in terms of f(x)?
b) What is the equation of g(x) in terms of x?
c) Then, g(x) is shifted 7 units down to obtain function j( x) . What is the equation of j( x) in terms of
d) What is the equation of j(x) in terms of x?
4 + 0.5t = 1.5 + 0.9t, solve for t
4 - 1.5 =0.9t - 0.5t
2.5 =0.4t divide both sides by 0.4
t = 2.5 / 0.4
t =6.25 - years, when population of both towns will be the same
2,000 + 6.25 =2,006.25 =~2,006 - the year in which both towns will have the same population.
c) Sub t in one of the equations:
4 + 0.5t =
4 + 0.5 x 6.25 =
4 + 3.125 =
=7.125 millions, or:
7.125 x 1,000,000 =7,125,000 - the population of both towns when they will be the same in ~ 2006.