MontgomeryCollege Mathematics

MA 101

Final Exam

Name: ______

Please show all necessary work to justify your answer.

(20 points)1. Given a linear equation .

a) Find the x-intercept and the y-intercept.

x-intercept: ( , )

y-intercept: ( , )

b) Find the slope.

c) Sketch the graph.

(12 points) 2. Let.

a) Find.

b) Find when .

(10 points)3. Find an equation of the line with slope 3 and passing through (1, 2).

(20 points) 4.The table below shows the number of employees for a software company from

1992 to 1997. Let represent the number of employees years since 1990.

Year / Number of employees
1992 / 110
1993 / 143
1994 / 170
1995 / 202
1996 / 241
1997 / 269

a) Use your calculatorto find the Best Fit Line(linear regression line) for the data.

(Make sure the graph of your line comes close to the points in the scattergram)

b) Find the -intercept. What does it mean inthe context?

c) What is the slope? What does it mean in the context?

d) Predict the number of employees in 2010.

(12 points) 5. Rewrite each expression in radical form then simplify.

a)

b)

(18 points)6. Simplify and leave no negative exponents in the answer. (Assume is positive)

a)

b)

c)

(18 points)7.All State life insurance offers a $25,000 life insurance policy for men who are smokers. The monthly rates are listed for various ages.

Age Rate($)

30 / 50.85
35 / 61.74
40 / 92.27
45 / 134.97
50 / 193.25
55 / 290.18
60 / 444.54
65 / 674.06

Let represent the monthly rate in dollars for a man t years of age who smokes.

a) Use your calculator to draw a scattergram of the data. What kind of function (linear,

quadratic, or exponential) would you like to use to model the data?

b) Use your calculator to find an equation for (Round your result to three decimal

places).

=

c) Find . What does it mean in terms of the context?

(12 points)8. Evaluate.

a)

b)

c)

(12 points)9.Suppose that 1000 dollars are invested in an account with interest rate 5.5%

compounded annually. Let represent the balance in the account at the end of

years. A reasonable model for is given by

Partial credit given for Calculator only answer. Full credit for algebraic solution.

a) How much is in the account after 6 years?

b) How long will it take for the account to grow to 2000 dollars?

(20 points)10. Let . Determine the following algebraically.

a) Find the x-intercepts.

b) Find the y-intercept.

c) Find the vertex.

d) Sketch by hand the graph of .

(18 points)11.A rental car company started business in 2000. Let represent the company’s

Profit in millions of dollars, where is the number of years since 2000. A possible

Model for is .

a) Predict the amount of profit in 2008.

b) In what year before 2006 did the company have 0 profit?

c) In what year will the company have maximum profit?

d) What is the maximum profit?

(28 points)12. Solve.

a)

b)

c)

d)

Bonus:

(+10 points) Solve the following system of equations algebraically or graphically.

1