Could anyone please help me with this.

Could you please provide full calculations for me to understand it well. For question 1, they say u to use hint but still I need the calulations for me to understand. Please provide calculation.

1. (a) Use technology to complete a table of values for y = 2* and - for -4 S x $ 4. dx Hint: Use - under Calc on the graphics calculator or other technologies. dx (b) Draw scatterplots of y = 2* and dy dx - on the same set of axes for -4 S x $ 4. (c) By inspection of the scatterplots in question 1.(b), give reasons why the derivative ( ) of y = 2* is an dx exponential function. (d) (i) Use modelling techniques to find the derivative function of y = 2*. It can be written in the form -= ab* (ii) Discuss the accuracy of your values of a and b. 2. Repeat the process in question 1. (leaving out part (b) and (c)) for: (i) y = (2.2)* (ii) y =(2.4)* (iii) y = (2.6)* (iv) y =(2.8)* (iv) y = 3* 3. Using questions 1. and 2. Suggest a relationship between exponential functions and their derivative functions. There is a function of the form y = a* that is its own derivative function, i.e. = dx 4. Find this function, with a to 5 significant figures using modelling techniques. Include evidence to support the result. 5. The value found part 4. is a special value. Research this value and write some basic facts about it