Math 135 Sample Exam #3
Spring 2007
NO graphing calculator is permitted. This exam is longer than the actual exam but covers all types of problems that may be given.
CHAPTER 4
1a) find
b) find the pH for grapefruit from the given hydronium ion
concentration is
c) use the change of base formula to find an approximation
d) lf we let write each expression in terms of without using the ln.
e) given that
2) The magnitude of an earthquake, measured on the Richter scale, is , where I is the amplitude registered on a seismograph 100km from the epicenter of the earthquake, and is the amplitude of an earthquake of a certain (small) size.
Find the Richter scale ratings for earthquakes having amplitudes:
a) b) c)
3) Solve each equation: give BOTH exact and decimal answers correct to 4 dec. places
3a)
3b)
3c)
3d)
3e)
3) Solve each eqn. (contd.)
3f)
3g)
3h)
3i) solve for x:
4. How many years, to the nearest tenth, will be needed for $3000 to increase to $7000 at compounded monthly?
5. How long will it take for a quantity of to decay to 25% of the initial amount, knowing that it decays according to the function defined as follows, where t is time in days?
6. Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only one-third the amount found in living human beings. How long ago did the Egyptian die when the half-life of carbon-14 is 5700 years?
7. Newton’s Law of Cooling is given by the following eqn. where f(t) is the temperature of the water at any time t after being introduced into an environment having constant temperature and C is the difference in temperature between the water and the environment around it.
If boiling water at is placed in freezer at , and the temperature of the water is after 24 minutes, find the temperature of the water after 60 minutes (change minutes to hours)
CHAPTER 5
1. Use the substitution method to solve the following system of equations;
2. Solve the following system of equations. Tell what you did to each row.
3. Use the Gauss-Jordan method to solve each system:show all steps and indicate what row operations etc.
3a)
3b)
4. Application problems like pg. 489, #91- #96
5. Evaluate the following determinants: show all steps
5a)
5b)
6a) Find the cofactor of each element in the second row for
6b) solve the following system as indicated by the following augmented matrix using Cramer’s Rule show all steps and tell what you are doing
7) Find the partial fraction decomposition of
8) Solve the following system of non-linear equations:
8a)
8b)
8c)
9) Graph the solution set of
10) Linear programming:
A company produces two models of lamps, A and B. They can produce up to 1500 lamps each day using no more than a total of 60 hours of labor. It takes 3 minutes of labor to make one model A lamp and 2 min of labor to make one B lamp. Graph the feasibility region and label the vertices.
How many of each model should be made daily in order to maximize the company’s profit if the profit on the model A lamp is $4 and the profit on the model B lamp is $3?