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 7Summary:
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.
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