Math 1101

Exam # 1, Summer ’01

Name____________________________________

  1. Which of the following relations in parts a - d are functions? Circle the letter a - d for those that are functions.
    1. f(x) = x2

      2.  

    2. g(x) = 2

      3.  

    3. h(x) = any number between 1 and 5.

      4.  

    x

    F(x)

    0

    0

    4

    3

    4

    1

 

x

G(x)

0

0

2

0

4

1

 

 

 

 

  1. Given the function f(x) = 3x + 5, find the value of f(-2). Answer_______________

    2.  

  2. Given the function:

x

G(x)

1

0

2

2

3

100

    1. What is the domain of G(x)? Answer__________

      2.  

       

    2. What is the range of G(x)? Answer__________

 

 

  1. Find an equation of the line that passes through the two points (0,4) and (4,0).

    2.  

    Answer___________________

  2. The population of Mathville was 100 in the year 1980 and 125 in the year 2000.

Assume the annual rate of change in population remains constant. Let t be the number of years since 1980. That is, t = 0 corresponds to 1980.
  1. Find the population function, P( t ) = P0 + mt.

    2.  

     

    Answer_______________________

  2. Find the population that is predicted by your function in the year 2010.

    3.  

     

    Answer_______________________

  3. In what month of what year will the population reach 137?

 

 

Answer_______________________

 
  1. The population P (in thousands) of a certain city in four different years is given below.

Date

1970

1980

1990

2000

P(Population in thous)

150

165

170

195
  1. Using the first and last points, calculate the average rate of change of the population per year.

    2.  

     

    Answer______________________

  2. Using the average rate of change from part a, find the population function , P’ ( t ) = P0 + mt, where t is the number of years since 1970. That is, t = 0 corresponds to 1970.

    3.  

     

    Answer______________________

     

  3. Fill in the table below with the predicted population using the function from part b above.

    4.  

     

    Year

    Time t

    Actual Pop P in thousands

    Predicted pop P’ in thousands

    Error P-P’

    Error squared

    1970

    		  

    150

    		      

    1980

    		  

    165

    		      

    1990

    		  

    170

    		      

    2000

    		  

    195

    		      

     

     

  4. Compute the sum of the squares of the errors, SSE.

    5.  

     

    Answer______________

  5. Compute the average error.

    6.  

     

    Answer______________

     

  6. Now use your calculator's linear regression function to find the "best fit" linear equation that fits the data.

    7. Answer____________________

     

  7. Fill in the table below with the predicted population using the function from part f.

    8.  

     

     

    Year

    Time t

    Actual Pop P in thousands

    Predicted pop P’ in thousands

    Error P-P’

    Error squared

    1970

    		  

    150

    		      

    1980

    		  

    165

    		      

    1990

    		  

    170

    		      

    2000

    		  

    195

    		      

     

  8. Compute the sum of the squares of the errors, SSE.

    9. Answer___________

     

     

  9. Compute the average error.

Answer___________