Can you please answer the following questions: 1. Bill has started a diet and lost 15 lbs in 10 weeks. What is his average weekly weight loss? State this as a rate of change. a). The rate of change of Bill's weight is -0.75 lbs per week. b.) The rate of change of Bill's weight is 1.5 lbs per week. c.) The rate of change of Bill's weight is -1.5 lbs per week. d.) The rate of change of Bill's weight is 0.75 lbs per week. 2. Suppose an object is moving along a path described by f(t) = 2t^3 + 3t^2 - 6t, where f (t) is measured in meters and time in seconds. What is the object's instantaneous rate of change at time t = 2 seconds? a.) The instantaneous rate of change at time t = 2 is 12 meters per second b.) The instantaneous rate of change at time t = 2 is 30 meters per second c.) The instantaneous rate of change at time t = 2 is 36 meters per second d.) The instantaneous rate of change at time t = 2 is -26 meters per second 3. Sue opens a bank account with $1 and an interest rate of 3% per year, compounded continuously. The amount of money in the account can be described by A=1e^(1.03)t . Assuming interest is being paid continuously, what is the instantaneous rate of change of the account at t = 10 years? a.) The instantaneous rate of change of the account at t = 10 years is $3 per year. b.) The instantaneous rate of change of the account at t = 10 years is $30,624 per year. c.) The instantaneous rate of change of the account at t = 10 years is $20 per year. d.) The instantaneous rate of change of the account at t = 10 years is $306 per year. 4. The rollercoaster rides at MathGames are all shaped liked trigonometric functions. Dan goes on the "2sine" ride; his height in meters is measured by d(t) = 5sin(2t). At t = sec, what is Dan's instantaneous rate of change? a.) Bill's instantaneous rate of change is 10 meters per second. b.) Bill's instantaneous rate of change is 0 meters per second. c.) Bill's instantaneous rate of change is -10 meters per second. d.) Bill's instantaneous rate of change is 5 meters per second. 5. An object is moving along a path that can be described as f(x)=1/x meters between x = 0.5 seconds and x = 2 seconds, where x is in seconds and f(x) is in meters. What is the object's instantaneous rate of change at x = 1.5? a.) The object's instantaneous rate of change at x = 1.5 seconds is 16/9 meters per second. b.) The object's instantaneous rate of change at x = 1.5 seconds is 16/9 meters per second. c.) The object's instantaneous rate of change at x = 1.5 seconds is 4/9 meters per second. d.) The object's instantaneous rate of change at x = 1.5 seconds is 4/9 meters per second. 6. For f(x) = tan(x), what is the instantaneous rate of change for x = ? a.) The instantaneous rate of change of tan(x) at x = , is 2. b.) The instantaneous rate of change of tan(x) at x = , is -1. c.) The instantaneous rate of change of tan(x) at x = , is 1. d.) The instantaneous rate of change of tan(x) at x = , is 0