# . BOX ALL FINAL ANSWERS ************************************************************************************

**1. (4 pts) **The population of Aurora, Colorado for the years 1960 through 2010 is included in the table.** **

** **

**Year x Population**

** **

1960 48,548

** **1970 74,974

1980 158,588

1990 222,103

2000 276,393

2010 325,078

** **

a. (0.3) Aligning the years so that ? = 0 in 1960, complete the middle column by entering the appropriate aligned ? value.

b. (1.0) Perform a linear regression using the aligned inputs from part a, and write the regression equation in the form ? = jQuery22406862623461736679_1592020884776 + ? where ? and ? are rounded to three decimal places.

Regression Equation: _________________________________________

c. (0.2) Record the coefficient of determination here (4 decimal places) : _________

d. (0.3) What does this coefficient of determination result tell you about the regression equation vs the data?

e. (0.3) Based on the regression equation (model), what is the rate of change in Aurora's population during this period?

f. (0.5) Using the model (unrounded regression equation) evaluate ?(45). Show algebraic work.

*g. *(0.2) Interpret your result in part f in the context of this problem. As a sentence. *[Assume we do not count fractions of residents.] *

*h. *(0.7) In which year did Aurora's population reach 250,000 residents. Show algebraic work.

2. Solve the equation algebraically (show all work): − ? = 6 ^{− ?} 3

__OPTIONAL BONUS (1 point, SHOW WORK. BOX FINAL ANSWER, NO PARTIAL CREDIT)__

Solve ? = for ?.

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