If anyone can help me with these questions, please do so. I would really appreciate it, thank you!

Questions 1. Using the methods described in the content of this activity, find the slope of the tangent to the curve y = 10" to complete the following table. a. X Slope of Tangent -2 -1 0 1 2 3 b. Plot the points, sketch a graph and find the equation of the derivative of this function. (When modelling, use a regression equation of the form y = k . 10* , where k = In10) 2. Using the exponential equation of the form y = 2" find the slopes of the tangent to this curve to complete the following table. a. X Slope of Tangent -2 -1 0 1 2 4 b. Plot the points, sketch a graph and find the equation of the derivative of this function. (When modelling, use a regression equation of the form y = k . 2* , where k = In2) 3. State the derivative, f(x), of the following functions : a) f(x) = 4* bj f(x) = 5* c) f(x) = 7* dj f(x) = 100*1. Using Desmos, graph the function of y = ex. State the characteristics of this function and include an screenshot of the function. Use the information from the discussion posts (above) if necessary in order to help understand this function. What is the value of the slope of the tangent at x = 1 for this curve. Other characteristics of this function can include domain and range, asymptotes and root(s), end-point behaviour and intervals of increasing/decreasing. 2. Using the graph of the function y = ex; a. Use Desmos to complete the following table to find the slopes of the tangent to this curve. X Slope of Tangent -2 -1 0 2 4 b. Using the Excel/Desmos method of generating the equation for these points, sketch the graph of the derivative and find the equation for the deriavtive function. State the derivative of y = ex. Attach in your Excel/Desmos file. 3. Given the following functions, state the derivative. a) f(x) = 5ex b) f(x) = 10ex c) f(x) = -4ex + 7x3 - 5x61. If you invest $7500 compounded continuously at 4% pa. how much will this investment be worth in 5 years? 2. How many years would you have to invest $1000 in order to double your money if you where offered 2.5% fa interest compounded continuously ? 3. A population of 500 E. coli bacteria doubles every 15 minutes. Use this information to find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model. (For assistance with this question, please visit the instructor's YouTube video]. 4. Using the curve that you constructed for the decomposition of Carbon 14 (in the previous lesson), find the age of a prehistoric cave painting discovered in the Lascaux Caves in southern France if the amount of Carbon 14 has decayed to 40% of it's original mass