8) The quantity of charge Q in coulombs (C) that has passed through a point in a wire at time t (measured in seconds) is Q = t3 2t2 + 6t + 2. Recall that the rate Coulombs/sec is called current, its units are amps. a) how much total change has passed by at t=2? b) how much total charge has passed by at t=6? C) what is the change in charge between t=2 and t=6? (1) what is the current (rate of charge per time) from t=2 to t=6? e) what is the current (rate of charge per time) at t=2? 9) The cost C in dollars to manufacture x pots is C = 2000+3x+0.01x2 + 0.0002x3 a) find the cost to make 0 pots (this is called the fixed cost) b) find the cost to make 100 pots c) find the change in cost between making 0 & 100 pots (1) find the rate of cost per pot between making 0 & 100 pots (this is called the average cost). ll e) find the rate of 'cost per pot at exactly 100 pots (this is called the marginal cost). equilibrium position 10) A block attached to a spring slides back and forth on a flat table (as in the diagram). Its position x (meters from equilibrium) at time t (seconds) is x=85in(itt/6). a) if x is positive, what does that mean? b) if 3: is positive, what does that mean? if 3): is 0, what does that mean? c) find the position at lsec and at Bsec. d) find the displacement (change in position) between [=1 and t=3 e) find the average velocity (rate of position per time) between t=1 and F3 0 find the velocity at time t=1 11) * If R denotes the reaction of the body to some stimulus of strengthx, the sensitivity S is defined to be the rate of change of the reaction with respect to x. A particular example is that when the brightness of a light source is increased, the eye reacts by decreasing the area of the 0.4 pupil. The experimental formula R=% has been used to model the dependence of R + x ' on x when R is measured in square millimeters and x is measured in appropriate units of brightness. (a) Find the sensitivity. (b) Illustrate part (a) by graphing both R and S as functions of x. Comment on the values of R and S at low levels of brightness. Is this what you would expect? 4