Northern Star Online Properties of Logarithms and Solving Exponential Equations Problems

You DO NOT need to show your work for these questions unless the question specifically asks you to.

Part 6-4: e and Natural Logarithms

2. Suppose $4449 is invested at 11% compounded continuously for 7 years. What is the annual yield percent to the nearest hundredth?

Answer: _____

3. Suppose $4449 is invested at 11% compounded continuously for 7 years. How much money will be worth after that time?

Answer: ­­­­­_____

6. The population of New Zealand in 1990 was about 3,376,000 with an average growth rate of 2.7%. If this growth rate continues, use the Continuous Change Model to predict New Zealand’s population in 2008.

Answer: _____

7. A satellite has a radioisotope power supply, with power output given by

P = 73e^-t/347

Where t is the time in days and P is the power output in watts.
What is the power output to nearest hundredth of a watt at the end of its first year?

Answer: _____

8. A satellite has a radioisotope power supply, with power output given by

P = 73e^-t/347

Where t is the time in days and P is the power output in watts.
When the power output drops below 8 watts, there will be insufficient power to operate the satellite. How many days will the satellite be operational?

Answer: _____

10. Explain HOW you would find the answer to ln e^7.1

Answer: _____

Part 6-5: Properties of Logarithms

Use the fact that log_a 4 = .782 and log_a 3 = .654 and the property of logarithms to answer the following for Questions 1- 4.

1. Evaluate log_a 3/4 =

Answer: _____

2. Evaluate log_a 48 =

Report your answer to the thousandth place.

Answer: _____

3. Evaluate log_a 27 =

Report your answer to the thousandth place.

Answer: _____

4. Evaluate log_a 3a⁴ =

Answer: _____

5. Find an expression for A that does not involve logarithms

ln A = 2 ln B – 4 ln C

Answer: _____

6. Write a linear function for log y which is equivalent to y = 400(1.08)^x

Answer: _____

7. Write a exponential equation in the form A = c*d^t equivalent to ln A = 1.7t + 8.2

Answer: _____

Part 6-6: Solving Exponential Equations

5. If you invest money at 12.3% compounded continuously. How many years, to nearest tenth, will it take to double?

Answer: _____

6. Which expression(s) could be entered into your calculator to produce a graph of y = log₇ x

Select one or more:

a. y = log 7/log x

b. y = log x/log 7

c. y = ln 7/ln x

d. y = x/7

e. y = ln x/ln 7

Answer: _____