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90% + Suppose f'(x) =12v1+4x where f (0) = 5. 1) Find the general antiderivative, f (x). 2) Use the initial value to find f (6). Acceleration due to gravity in feet per squared second is the constant function a(t) = -32. Suppose a projectile is launched from a height of 100 feet with an initial velocity of 40 feet per second. 3) Find the velocity function, v(f), for the projectile. 4) Find the vertical position function, y(t), for the projectile. 5) When will the projectile hit the ground? T. The population of a town grows at a rate defined by the differential equation = 0.6t , where P is the population in thousands of people and t is the number of years. 6) Find the general solution to the differential equation. 7) If the current population of the town is 20,000, what will the population be in 5 years? Suppose the differential equation = 2"- where y(0) = 0. 8) Create a slope field the differential equation in a [0, 1] x [0, 1] viewing window. 9) Sketch a solution curve that passes through the point representing the initial value. 10) Use the solution curve through the initial value's point to approximate y(1)