Assignment 1 :Discussion Post
In this assignment, you will acquire the skills and knowledge to identify logarithmic and exponential functions.
Up to this point, in your exploration of higher-order polynomials, you’ve likely grasped that these functions don’t consistently exhibit linear growth or decay. Instead, their growth or decline can manifest in diverse patterns. You can gain a deeper understanding of these varied growth and decay phenomena through the lens of exponential and logarithmic functions. You will understand the applications of these functions in practical situations, including the growth of populations, compound interest, radioactive decay, and in pH levels in chemical solutions, etc.
You are required to complete all questions in this assignment, answer the following questions, and show stepwise calculations.
Task 1.
Earthquakes are complex phenomena, and we do not intend to provide an exhaustive discussion of the scientific principles behind them. We will present a simplified explanation of the Richter scale, The Richter scale measures the magnitude of an earthquake by comparing the amplitude of the seismic waves of the given earthquake to those of a “magnitude 0 event”, which was chosen to be a seismograph reading of 0.001 millimeters recorded on a seismometer 100 kilometers from the earthquake’s epicenter.
Specifically, the magnitude of an earthquake is given by
where x represents the seismograph reading in millimeters of the earthquake recorded 100 kilometers from the epicenter.
Using the above data, answer the following questions:
(a) Calculate the earthquake reading on the seismograph (using the M(x) function) when the magnitude of earthquake on the Richter scale 7.7 and 5.7. Compare the readings and conclude on the magnitudes of earthquakes based on the calculations obtained for both scale readings.
(b) In finding the magnitude of the earthquake, the experts have used the logarithmic function. In your opinion, discuss why this logarithmic function is used in describing this situation, and why not any other polynomial or exponential function used in describing the earthquake situation.
(c) Locate a new article discussing a recent earthquake in your country providing Richter scale magnitudes (You can also use an article that discuss country close to yours if there hasn’t been an earthquake in your country recently). Determine the seismograph reading by the magnitude of the earthquake registered in your country. Discuss the situation in brief.
Your Discussion should be a about 250 in length. Please include a word count. Following the APA standard, use references and in-text citations for the textbook and any other sources
Assignment 2: Math assignment
This assignment serves as an opportunity to assess your ability to identify exponential and logarithmic functions. Among the various functions you’ve studied, exponential and logarithmic functions hold particular significance when it comes to representing practical situations marked by non-linear and rapid changes. Recognizing logarithms as the inverse of exponential functions will enable you to solve equations involving exponential functions using logarithmic properties.
Within this assignment, you will delve into the properties of logarithms and acquire the skill to express scenarios using either exponential or logarithmic functions.
You are required to complete all the 3 tasks in this assignment, answer the following questions, and show stepwise calculations. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool for drawing the graphs.
Task 1.
Please answer the following questions related to exponential and logarithmic functions:
(i)What are exponential and logarithmic functions? How are they related? What are their key factors (Explain the variables used in the definitions of these functions)? Discuss their domain and range.
(ii) What is the difference between exponential, logarithmic, and power functions? Provide one mathematical example for each and illustrate the differences of growth patterns and any special points (such as asymptotes, intercepts, and zeros), if applicable. Graph the examples.
(iii)How to explain if a function has exponential growth?
(iv)Between exponential and logarithmic functions, which one grows faster? Provide an explanation for your answer.
(v) Write the observations of growth patterns and special points (if any) by drawing the graphs for the examples given
Task 2. Before working on task 2, please read the following reading:
Reading section 4.1- Exponential Growth and Decay of the following textbook will help you in understanding the concepts better.
Yoshiwara, K. (2020). Modeling, functions, and graphs. American Institute of Mathematics. https://yoshiwarabooks.org/mfg/frontmatter.html
Write the logarithmic properties at each step to solve the following questions:
(i) Simplify using logarithmic properties,
(ii) Condense the complex logarithm into single term
(iii) Solve:
Task 3. A research laboratory has been conducting experiments on the rapid increase of cancer cells in an animal. They have observed that cancer cell growth increases by 2% every year with certain medication. Initially, in the year 2018, there were 232.26 units of these cells in the animal.
Using the above data, answer the following questions:
(i) Create a table to illustrate the yearly increase in cancer cells up to the year 2023.
(ii) Examine the table of values and identify the mathematical function that represents this growth pattern, specifying the key factors of the mathematical function.
(iii) Utilize this mathematical function to project the level of cancer cells in 10 years, assuming the growth rate continues at the same pace.
(iv) Illustrate the growth pattern by plotting a graph (Take scale 100units on X and Y-axes).
Submission Settings:
Please complete all the 3 tasks in this assignment.
You may use a word document that addresses the questions mentioned above. Read the rubric on how you are going to be graded on this assignment.
Use APA citations and references if you use ideas from the readings or other sources. For assistance with APA formatting, view the Learning Resource Center: Academic Writing.
The document should be double-spaced in Times New Roman font, which is no greater than 12 points in size.
Use high-quality, credible, relevant sources to develop ideas that are appropriate for the discipline and genre of writing.
PLEASE COMPLETE THE 2 ASSIGNMENTS SEPARATELY ( SEPARATE DOCUMENTS)WITH A REFERENCE PAGE ON BOTH OF THEM. THEY WON’T BE HANDED IN TOGETHER.
