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 m(x) = .5(3x) and the derivative function m(x). What is the formula for d/dx (.5(3x))? How can you confirm this using Desmos? (b) (Part 3 ) Explain the steps you used to find the function P (x) 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 P (x), evaluate this derivative for April, and explain in words what this represents.

For part (b) and (c), the graph and the table is in the image below-

and p(x)= k(b^x)