1. MATH 110
EXAM 3 Review

2. Jeopardy 100 200 300 400 500 Oh Rats Show me the Money The Big “e”
Who are those guys?
Famous Log Cabins
It’s all Greek to Me!
100
200
300
400
500

3. Oh Rats 100
Find the domain for the function:
Answer: x ≠ 7, -2

4. Oh Rats 200 Find all asymptotes and intercepts to the function:
Answer: V.a. at x = -2, (-1/7). H.a. y = (-4/7). X-int at x = ± √(5/4). Y-int at (0,2.5)

5. Oh Rats 300 Find the equation of the slant asymptote for the function
Answer: y = 7x + 29

6. Oh Rats 400
Find the equation for a rational function with: (1) vertical asymptotes of x = 2, -3 (2) x – intercept (4,0) and a (3) horizontal asymptote of y = 0.
Answer:

7. Oh Rats 500
Find the equation of the rational function shown:
Answer:

8. Show Me the Money 100
How much money should you invest at 6% compounded quarterly so that you have $20,000 after 9 years?
Answer:$11,701.79

9. Show Me the Money 200
Suppose $10,000 was invested in a trust fund for a child. After 20 years, the fund has matured to a value of $27, What is the interest rate of the fund if interest has been compounded continuously?
Answer: 4.99%

10. Show Me the Money 300
Suppose you wish to invest $6000 at 7.8% interest for 3 years. What is the difference in the value of your investment after 3 years if you invest it compounded continuously as opposed to compounded weekly?
Answer: The continuous compounding is $1.33 higher than the weekly compounding.

11. Show Me the Money 400
How long does it take for a $10,000 US Treasury Bond earning interest at 2.4% compounded monthly to mature to $15,000?
Answer: Around 17 years

12. Show Me the Money 500
The effective annual yield is a number that banks like to quote when comparing different accounts. This number tells you the percentage growth you can expect to see each year on your account. Consider the following two accounts: (1) $25,000 invested for 1 year at 7.6% compounded quarterly (2) $25,000 invested for 1 year at 7.2% compounded monthly. What is the effective annual yield for each account? Which would you choose?
Answer: account 1: 7.82% ; account 2: 7.44%; choose account 1.

13. The Big “e” 100
Plutonium-240 is a radioactive material whose decay is modeled according to the exponential function:
t is in years
What is the half-life of plutonium-240?
Answer: years

14. The Big “e” 200
One hundred kilograms of a certain radioactive substance decays to 40 kilograms after 10 years. If the amount of the substance is modeled by the exponential function , what is the rate of decay?
Answer: r = or the substance decays at a continuous rate of 9.163% annually.

15. The Big “e” 300
The air in a factory is being filtered so that the quantity of a pollutant P (mg/liter) is decreasing according to the exponential function where t is in hours. If 10% of the pollution is removed in the first 5 hours, how long until the pollution is 50% of its original value?
Answer: 33 hours

16. The Big “e” 400
When a murder is committed, the body, originally 37 degrees C, cools to 35 degrees C after two hours. Suppose that the police find the body at 4 pm and find that the body temperature is 30 degrees C. If the temperature of the surrounding air is a constant 22 degrees C, determine when the murder was committed?
Answer: 7:13am

17. The Big “e” 500
Radium has a half-life of 1,620 years. If 1000 grams are initially present and the amount of Radium can be modeled by the exponential function , how much of the substance would remain after 1000 years?
Answer: grams

18. Who are those guys? 100
Which of the following represents a one-to-one function?
(1)
The function f which assigns each U of A student his/her student I.D. number

19. Who are those guys? 200 Find the inverse for the function below:
Answer:

20. Who are those guys? 300
Suppose the function L(x) gives a person’s life expectancy when they are born x years after Find a formula for the inverse and explain what this function represents.
Answer: The inverse tells you the year you were born given your life expectancy.

21. Who are those guys? 400
The graph below shows the equation of a logarithmic function. Find its equation.
Answer:

22. Who are those guys? 500
Find the inverse of the function
Answer:

23. Famous Log Cabins 100
Simplify each expression:

24. Famous Log Cabins 200
Expand the following logarithm completely:

25. Famous Log Cabins 300
Write the following as a single logarithm:

26. Famous Log Cabins 400
Which of the following is/are true?

27. Famous Log Cabins 500
Solve for x:
Answer: x = -1

28. It’s All Greek to Me 100
The number of rabbits (in 100s) in a rural area for several months is shown:
Assuming that the population will grow exponentially, find the doubling time for the rabbit population. How fast does the population grow each month?
Answer: Doubling time: 1.3 months; rate of growth 72% a month! (That’s a lot of rabbits) t 1 2 3 4 5 Q 25 43 74
127
219
376

29. It’s All Greek to Me 200
The current population of a certain town is 10,000 people. The population has been growing annual at a rate of 5% each year and is modeled by the function How long until the population doubles from its present value?
Answer: 14 years

30. It’s All Greek to Me 300
Before kerosene can be used as jet fuel, federal regulations require that the pollutants in it be removed by passing the kerosene through clay. Suppose that the clay is in a pipe and that each foot of pipe removes 20% of the pollutants that enter it. Write an exponential model of the form to show how much pollutant would be left from an initial quantity of 100 grams.
Answer:

31. It’s All Greek to Me 400
An almanac lists the world’s population in 1980 as billion people and in 1994 as billion people. What is the doubling time of the world’s population?
Answer: 42 years

32. It’s All Greek to Me 500
A picture supposedly painted by Vermeer ( ) contains 99.5% of its carbon-14. If the half-life of carbon 14 is 5730 years, determine whether or not this picture is fake.
Answer: It’s a fake!