MA101 Exam 3 - Chapter 5 – Fall 2010 Name______
I am evaluating your algebra skills. I am not evaluating your ability to guess.
It is very important that you show all work – be organized and neat
1. A person invests $20,000 in an account at 9% interest compounded annually. When will the value of the investment be $50,000? Use algebra to answer.
A storage tank contains a radioactive element. Let p = f(t) be the amount (in grams) of the element that remains at t years after today. The graph for f is shown below:
The amount (in grams) of the radioactive substance left in the tank after t years can be modeled by the function
a) How many grams of the radioactive substance does the tank contain today? Use proper units - Show work. Use the function to answer, then, check with the given graph to see if the answer is correct.
b) When will there be 20 grams left in the tank? Round to the nearest tenth and use proper units - Show algebraic work
a) Use the function to answer, then, check with the graph to see if the answer is correct.
2. Rita makes some coffee at home, pours some in a cup and takes it with her to her bedroom to study math. The coffee’s temperature y (in degrees Fahrenheit) is given by
; where t is the number of minutes since Rita made the coffee.
a) What is the temperature of the coffee when she made it? Write proper units.
b) Rita decides to drink her coffee when it reaches a temperature of 144 . How long will she have to wait to drink her coffee? Show algebraic process to solve – include units in your answer.
c) Rita was so enthusiastic about her math homework that she forgot about her coffee. Forty five minutes later, when she finished her math homework, she checked on the coffee again. What was the temperature of the coffee at this time? Show work and write proper units in your answer.
d) If Rita does not drink her coffee, what is the lowest temperature that the coffee will reach? Think; play with it to get an answer. What do you think this temperature represents? Use common sense to answer this last question.
3. a) Construct a table of values for the function
b) Plot the ordered pairs and graph the function.
c) Construct the table for the inverse function and graph on the same coordinate system
d) Write the equation for the inverse function
X /-2
-1
0
1
2
/ / X / =......
Which one is the inverse function of ? Circle one
e) Use the given function to find f) Use the table to find
4. Find the inverse algebraically – show work and write answer using function notation
5. The graph of y = f(x) is shown below.
USE THE GRAPH to answer the questions
a) You are familiar with graphs of functions. Is this the graph of an
a. Exponential or a logarithmic function? Circle one
READ THE GRAPH and answer
b) Find f(4) b) Solve f(x) = 1 c) Find
6. Use the calculator to evaluate the following. Write the answer using 6 decimal places. Then, write the exponential equivalent.
a) = the exponential equivalent is:
b) Log 25 = the exponential equivalent is:
c) Ln 32 = the exponential equivalent is:
7. Solve the following equations - show algebraic work. Write the answer with ALL the decimals you get in the calculator
8. This is about forgetting in a Math class – does this happen to you?
Students in a Math class took a final exam. Without reviewing the material, they took equivalent forms of the exam at monthly intervals.
The average score S(t), in percent, after t months was found to be given by
S(t) = 70 – 20 ln(t+1) , where t is zero or more
a) What was the average score when they initially took the test, t = 0?
b) What was the average score after 5-months? Use one decimal place.
c) Graph the function S(t) = 70 – 20 ln(t+1), label axes with words and units. Use the window [0,20] for x and [0,90] for y.
d) After what time t was the average score 50%?
Use the graph and the INTERSECT feature of the calculator to answer – Show the details of the solution and the answer on the graph of part (c). Round to one decimal place and use proper units.
9. The loudness of sound can be measured on a decibel scale. The sound level L (in decibels) of a sound is given by where I is the intensity of the sound (in watts per square meter, W/
a) The intensity of sound inside a racecar reaches 10 W/ . How loud, in decibels, is this sound level?
b) Any sound level of 85 decibels or more is unsafe. Is the sound level inside of a race car unsafe? Explain why or why not.
4). The following table gives numbers of methamphetamine Labs cleaned up by Toxic spill crews in Washington.
Year #of labs
1995 / 421996 / 146
1997 / 208
1998 / 350
1999 / 792
2000 / 1458
a). Let represent the number of methamphetamine Labs cleaned up by Toxic spill crews in Washington in the year t years from 1995. Draw a scatter gram on calculator; is it better to use a linear model or an exponential model?
b). Find an equation for .
c). What does the base, b, of the function tell you about the number of labs?
d). Use to predict when the number of meth labs cleaned up by TSCs is equal to the number of households in Washington.( There are 2.2 million households)
3). The speed of a computer depends on (among other things) its chip speed. The speeds of various chips in MHz and when they were first available are listed in the table below.
Year MHz
1987 / 0.11989 / 2
1991 / 12
1993 / 16
1995 / 50
1997 / 120
1999 / 300
2001 / 1000
Let represent the speed of a chip at t years since 1971.
a). Use a graphing calculator to draw a scatter gram of the data. Is it better to model the data using a linear or an exponential function? Explain
b). Find an equation for . Hint: Using your calculator ( expReg) Use 2 decimal places.
c). According to your model, when will the chip speed be approximately 9000MHz?
d). Interpret the y intercept of the model.
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