**DS 1 **

- What is a natural logarithm? How is it different from and similar to regular logarithms? Provide examples for how natural logarithms appear in nature or in natural science.
- What are two applications of logarithmic and exponential functions in science?

**DS 2**

What is the relationship between exponential and logarithmic functions? Include examples.

**DS 3**

Graph two logarithmic functions with different bases and their corresponding exponential functions. What are the similarities and differences in the graphs?

**DS 4**– Exponential Functions

- Graph the function.

- Graph the function.

- Find the accumulated value of an investment of $8500 if it is invested for 3 years at an interest rate of 4.25% and the money is compounded monthly.

- Find the accumulated value of an investment of $1200 if it is invested for 6 years at an interest rate of 6% and the money is compounded continuously.

**DS 5-** Logarithmic Functions

- Evaluate
- Evaluate
- Graph the function.
- Find the domain of

**DS 6**– Exponential Functions

Let **R** be the response time of some computer system,

**U** be the machine utilization (CPU),

**S** be the service time per transaction,

**Q** be the queue time (or wait time… pronounced as my last name, Kieu) and

**a** be the arrival rate (number of log-on users).

The total response time (excluding network delay) is the sum of queue time and service time. Thus,

**R = S + Q **(1)

Generally, the service time is predictable and relatively invariant. The time a transaction spends in queue, however, varies with the transaction arrival rate a. Assuming that the arrival and service processes are homogeneous (time-invariant), the following is true:

**R = SQ + S **(2)

According to Queuing Theory (Allen, 2014):

**Q = a * R** (3)

Manipulating equations (2) and (3) using Factoring method, we obtain: ** **

** ****(4)**

- Show how you manipulate the two equations (2) and (3) to arrive at (4).
- Create a graph for (4), discuss observations, and make interpretations of this graph.

** **

**DS 7**Summary:

**Week3**

**Exponential & Logarithmic Functions**

Objectives/Competencies

3.1: Solve exponential and logarithmic functions.

3.2.Graph exponential and logarithmic functions.

3.3 Apply exponential and logarithmic functions to real world problems.

- What do you think you have learned in Week 3? Math skills? Online skills? Others?

**2**. What was the most useful and practical concept learned in Week 3 that you can easily relate to your real life and/or work experience? Please substantiate.