1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. These questions refer to Lab 7: Exploring Derivatives of Exponential Functions (a) (Part 2) Show the graph of the function(x) = .5(3x) and the derivative function m'(r). What is the formula for d (.5(37))? How can you confirm this using Desmos? (b) (Part 3) Explain the steps you used to find the function(r) to model the price of gas in the first 6 months of 2022. What does your function predict for April 2022 (month 3)? How does this compare to the source data? (c) (Part 4b) Explain how to find a formula for(r), evaluate this derivative for April, and explain in words what this represents. (d) EXTRA CREDIT: (Part 7)What is Euler's constant,e? Explain what is special about the derivative of the functionf(r) =er, and how you know this