03 Jul calculus

1. A minivan was purchased for $32,000. If the value of the minivan depreciates by $1,700 per year, find a linear function that models the value V of the car after t years. Use the function and find the value of the car after 5 years.2. Simplify tan x(csc x – sin x)3. A research lab grows a type of bacterium in culture in a circular region. The radius of the circle, measured in centimeters, is given by , where t is time measured in hours passed since a circle of a 1cm radius of the bacterium was put into the culture. Express the area, A(t), of the bacteria as a function of time, and find the approximate area of the bacterial culture in 4 hours.4. A pendulum moving in simple harmonic motion is modelled by the function , where  is measured in inches and t is measured in seconds. Determine the first time when the distance moved is 4 inches.5. Solve .6. Estimate the slope of the tangent line to  at x =2 by finding the slope of the secant line through (2,f(2))  and (2.001,f(2.001))