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.htmlWrite the logarithmic properties at each step to solve the following questions:(i) Simplify using logarithmic properties,ii)Condense the complex logarithm into single termiii) Solve

(i) Simplify using logarithmic properties,(ii) Condense the complex logarithm into single term(iii) Solve:

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

Instructions: Graph the following function. Then, state whether the function represents exponential growth or decay.y=11x𝑦=11𝑥This function is exponential

Let’s do an example together that is an exponential decay model.ProblemThe cost of a new car is $32,000$32,000. It depreciates at a rate of 15%15% per year. This means that it loses 15%15% of its value each year.Draw a graph of the car’s value against time in years.Find the formula that gives the value of the car in terms of time.Find the value of the car when it is four years old. SolutionThis is an exponential decay function. Start by making a table of values. To fill in the values we start with when t=0𝑡=0. Then we multiply the value of the car by 85%85% for each passing year. (Since the car loses 15%15% of its value, it keeps 85%85% of its value. 100−15=85100−15=85.) Remember 85%=0.8585%=0.85.Time Value (Thousands)0032321127.227.22223.123.13319.719.74416.716.75514.214.2The general formula is y=a(b)x𝑦=𝑎(𝑏)𝑥. In this case y𝑦 is the value of the car, x𝑥 is the time in years, a=32,000𝑎=32,000 is the starting amount in thousands, and b=0.85𝑏=0.85 since we multiply the value in any year by this factor to get the value of the car in the following year. The formula for this problem is:y=𝑦= (( )x)𝑥Finally, to find the value of the car when it is four years old, we use x=4𝑥=4 in the formula. Remember the value is in thousands.y=32000(0.85)4=𝑦=32000(0.85)4= At 44 years old, we expect the car to be worth $$ CheckQuestion 2

Identify each type of decay as linear or exponential.(a) Decreasing by 20% each yearlinearexponential    (b) Decreasing by 700 units each yearlinearexponential    (c) Half remains each yearlinearexponential    (d) Multiplying by 18 each yearlinearexponential