MATH176 Logarithmic and Exponential Function

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Complete discussion board questions for pre-calculus. I have attached the questions below.

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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.

2. What are two applications of logarithmic and exponential functions in science?

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

DS 1 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. 2. 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 1. Graph the function. f ( x) = 2 x −1 + 1 2. Graph the function. f ( x) = e x − 2 3. 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. 4. 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 1. Evaluate log 27 9 2. Evaluate 6 log 6 15 3. Graph the function. h( x) = log 2 ( x − 1) 4. Find the domain of f ( x) = log 4 ( x + 2) 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: R= S 1 − aS (4) 1. Show how you manipulate the two equations (2) and (3) to arrive at (4). 2. 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. 1. 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.

Tutor Answer

achiaovintel
School: New York University

kindly find the attached document. In case of any question feel free to ask.Thank you

Running Head: LOGARITHMIC AND EXPONENTIAL FUNCTIONS
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Logarithmic and Exponential Function
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Institution
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LOGARITHMIC AND EXPONENTIAL FUNCTIONS

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DS 1- Natural and Regular Logarithms
The natural logarithm is any logarithm whose base is a unique number e (Euler’s
number) that represents a fixed irrational number approximated as 2.718281828459.
Natural and regular logarithms are similar in that, they exhibit the same logarithmic
properties. The only difference is the base used (Kuhlmann & Tressl, 2012). Where
natural logarithm uses base e, regular logarithm uses base 10. An example of how natural
logarithm appears in natural science is the decay equation of the radioactive material.
The decay equation is a shown below:
I = Io e−rt
where: I is the amount of radio active material after the decay
Io is the intial amount of the radio active material
r is the rate of decay and t is the time taken.
The two application of log...

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