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 finish 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 M(x)= \log_1_ 0 (\frac{x}{0.001})

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.