2. The profit for a particular company over a 4 year time span could be modeled by P(t) = ln(t2+4)+3 0 5 1:54 where P is measured in millions of dollars and t in years. (a) Demonstrate the chain rule by finding P'(t). (b) Rewrite P'(t) in power form, then demonstrate the product rule to find P\"(t). Write out the first and second functions and their derivatives to show the work of finding P"(t). Do not simplify the result. Notate your answer. (c) Find P\"(1.8) and P\"(2.2). Write a sentence to explain what you can deduce from these results about the rate at which the company's profit is growing near the time when t = 2? 3. At the start of October 2021. cumulative number of COVIDlg cases for the state of Idaho are recorded every 2 days in the chart below. Use this data to answer the following questions. total cases 268,660 (a) Find a good approximation of the ROC at t = 4. Include units. (b) Write the linearization for the total number of COVlD19 cases statewide at t = 4. (c) Find the linear approximation for the total number of COVlD19 cases statewide at t = 5. (d) If the actual number of cases statewide at t = 5 is 263,294. what is the error in the approximation found in part (c)