Please show all steps and formulas used!! Thank you in advance

1. The cumulative sales S (in thousands) of a new product after it has been on the market for t years are modeled by S =50(1-e*'). During the first year, 8000 units were sold. a) Solve for k in the model. b) How many units will be sold after 5 years? 2. Use the given information to write an exponential equation for y. Does the function represent exponential growth or decay? Explain your answer. dy dt -=-4y, y=30 when t = 0. 3. Find each of the following indefinite integrals. a) [(x' -8x' + 10) dx 6) (12x -3dx 4. Find each of the following indefinite integrals. a) [x' (2x' -1)'dx 3 b) ) 7x - 2 -dx 5. Find the profit function for the given marginal profit and initial condition. Marginal Profit Initial Condition dP =-18x+1650 P(15) = $22, 725 dx