MA153 Final Assignment

YOU NEED TO SHOW ALL OF YOUR WORK TO GET CREDIT

1.      Find an equation for the straight line that passes through the points (-3,6) and (5,-4).

2.      Suppose that the population of a city is growing exponentially fast. Suppose that at the beginning of the year 2000, the population was 10,000 people and that at the beginning of 2008 the population was 15,000 people.  Let P=f (t) be the population t years after 2000.

a.       Find a formula for the population as a function of time t.

b.      Determine the annual percent growth rate of the population.

3.      Let .  Compute each of the following and simplify as much as possible.

a.       g(-3)

b.      g(b)

c.       g(b-2)

4.      Solve the equation  algebraically

5.      One hundred people are in line.  Let A be the set of integers from 1 to 100, in other words, A={1,2,3,…,99,100}.  Let B be the set of all first names of people.  Let f be the function that, to each number m in A, assigns the first name of the person who is the mth person in line.  Suppose John is the twentieth person in line and Sally is standing somewhere near the middle of the line.  Answer the following questions.  Explain completely.

a.       What does f(1) tell you?

b.      What does f(100) tell you?

c.       What is f(20)?

d.      Suppose Sally is the mthperson in line.  What does f(m+2) tell you?

e.       Suppose Sally is the mth person in line.  What does f(m-2) tell you?

f.       For which numbers  will f(m+2) not make sense?

6.     

a.       Find the midpoint of line segment PQ.

b.      Find the length of line segment PQ.

c.       Find the equation of a line that is perpendicular bisector of line segment PQ.

7.      Look at the table below concerning the function f and answer the questions below:

a.       What is f(5)?

b.      Is there a number c with the property that f(c) =50?  If so, what is the number c.

c.       Could the table be linear? Show your work for each increment.

8.      For each of the functions below, determine the domain and range.

a.    

                                                                                          Domain:

                                                                                          Range:

b.    

                                                                                          Domain:

                                                                                          Range:

c.     

                                                                                          Domain:

                                                                                          Range:

d.    

                                                                                          Domain:

                                                                                          Range:

9.      Consider the function f defined by

Answer the following questions concerning f.

a.       f(0)=

b.      Find a number c such that f(c)=12

c.      

d.      Find the average rate of change of f on the interval

e.       Graph f.  What is the domain and range of f?

10.  Let

a.                                                             b.

11.  Let

a.       Determine a formula for the inverse function .

b.     

c.      

12.  Determine the concavity of  from x=0 to x=6 by increments of 2

13.  Find the zeros of the following functions by the method indicated

a.                (Using the factoring method)

b.                (Using quadratic formula method)

14.  Write an exponential function that fits these two points (using a calculator to give the equation will not work, show your steps!)

15.  Suppose you invest $3981 in an account that earns 2.9% interest.  Determine the EFFECTIVE RATE and calculate how much money you will have in your account after t years and 5 years if the money is compounded:

a.       Daily

b.      Continuously

16.  Find the exact solution for x

a.                                            b.