1. Determine the equation of the normal line to () = (x^3)(3.5^-3x) at x=-12. A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount is, A(t)= 100(1.3)^-1.a) What is the half-life for this substance? Round to 2 decimal places.b) Determine the rate of decay after 10 years. Round to 2 decimal places.3. Given () = 2^x cos , 0 , find the critical point(s) on the given interval. If necessary, round your final answer(s) to the nearest hundredth of a radian. Identify the nature of the critical point(s).4. Explain two different ways to solve for the derivative of () = 200sincos5. Explain the steps you would take to find the derivative of () = (1/2)e^(-3x^2+tan(3x+5))

1. Determine an expression for the area of a rectangle inscribed in a circle of radius 1 cm, in terms of angle ch as shown in the diagram below and be sure to state any restrictions on q). [T! b} Determine the maximum area of the inscribed rectangle. [Tl