Suppose the position of an object moving horizontally after t seconds is given by the following function s =f(t), where s is measured in feet, with s > 0 corresponding to positions right of the origin. a. Graph the position function. h. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the le? 0. Determine the velocity and acceleration of the object at t: 1. d. Determine the acceleration of the object when its velocity is zero. e. On what intervals is the speed increasing? f(t)=8t-2'12;Osts7 An object thrown vertically upward from the surface of a celestial body at a velocity of 15 mls reaches a height of s = - 0.3t2 +15t meters in tseconds. 3. Determine the velocity v of the object after t seconds. b. When does the object reach its highest point? c. What is the height of the object at the highest point? d. When does the object strike the ground? a. With what velocity does the object strike the ground? f. On what intervals is the speed increasing? E> Suppose the position of an object moving horizontally after t seconds is given by the following function 5 = f(t), where s is measured in feet, with s > 0 corresponding to positions right of the origin. a. Graph the position function. h. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left? c. Determine the velocity and acceleration of the object at t= 1. d. Determine the acceleration of the object when its velocity is zero. a. On what intervals is the speed increasing? f(t)=t3 12t2 +451; 05ts7 The population ofa certain state (in thousands) from 1991 (t= O) to 2001 (t= 10) is modeled by the polynomial p(t) = -0.26t2 + 115t+ 6713. a. Determine the average growth rate from 1991 to 2001. b- What was the growth rate for this state in 1993 (t = 2) and 2001 (t = 10)? c. Use a graphing utility to graph p' for OS t S 10. What does this graph tell you about population growth in this state during the period of time from 1991 to 2001? Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. c. Interpret the values obtained in part (b). C(x) = 0.04;:3 + 0.4x2 + 50x +110, 0 Ex 51500, a = 800 3. The population of the state of Georgia (in thousands) from 1995 (t = 0) is modeled by the function p(t) = 0.27t2 +10t + 7055 . a. Determine the Population of Georgia in 2000 b. Determine the average growth rate om 1995 to 2005. c. What was the Instantaneous growth rate for Georgia in 1997 and 2005? d. When will the population decrease? 5. Find the equation of the tangent line to the graph of f(x) = X at x+3 X f (x) =1 x+3