1. MATH 109 Test 2 Review

2. Jeopardy Show me the $$$$$ Exponential Applications Famous Log Cabins
Potpourri
100
200
300
400
500

3. 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

4. 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%

5. 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.

6. 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

7. Show Me the Money 500
How long does it take for an investment of $5000 to double if it is invested at a rate of 7.5% compounded quarterly?
Answer: Around 9 years

8. Exponential Applications 100
Plutonium-240 is a radioactive material which takes a long time to decay. If you have 100 grams initially, 1 year from now you’ll have grams. Assuming that Plutonium-240 decays exponentially, what is its half-life?
Answer: years

9. Exponential Applications 200
One hundred kilograms of a certain radioactive substance decays to 40 kilograms after 10 years. If the amount of the substance is decaying exponentially, what is the annual decay rate?
Answer: 8.76% annually

10. Exponential Applications 300
The air in a factory is being filtered so that the quantity of a pollutant P (mg/liter) is decreasing exponentially. If 10% of the pollution is removed in the first 5 hours, how long until the pollution is 50% of its original value? Assume that originally there was 100 grams initially present.
Answer: 33 hours

11. Exponential Applications 500
Fill in the table (assume all initial values are 100):
Growth or Decay
Growth/Decay Factor
Growth/Decay Rate
Decay
23%
Growth
1.05
0.76
Growth or Decay
Growth/Decay Factor
Growth/Decay Rate
Growth
1.2
20%
Decay
0.4
60%
0.77
23%
1.23
1.05 5%
0.76
24%

12. Famous Log Cabins 100
Simplify each expression:

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

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

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

16. Famous Log Cabins 500
Solve for x using logs:
Answer: about 2.5

17. Potpourri 100
A population of lemmings declined from 100,000 to 75,000 in 3 months. Assuming an exponential decline, find a model for the lemming population as a function time. What is the decay rate each month?
Answer: 9.1% decline each year

18. Potpourri 200
The cost of tuition at four-year public universities has been increasing roughly exponentially for the past several years. In 1997, average tuition was $3,111 while in 2004 it was $5,132, a growth of about 65% over a 7 year period. Assuming this trend continues every 7 years, at what rate is tuition increasing each year.
Answer: %

19. Potpourri 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 function to show how much pollutant would be left from an initial quantity of 100 grams.
Answer:

20. Potpourri 400
An almanac lists the world’s population in 1980 as billion people and in 1994 as billion people, a growth of about 26% during this 14 year period. Assuming this trend will continue, what is the doubling time of the world’s population?
Answer: 42 years

21. Potpourri 500
The graphs and equations of three exponential functions are shown
List the growth factors from smallest to largest.
w, j, p
What can you say about V, Z, and T?
All are equal

22. Final Jeopardy
A culture of bacteria originally numbers 500 spores. After 2 hours there are 1500 bacteria. Assuming the number of spores grows exponentially, how long until the spores quadruple?
Answer: about 2.5 hours