Apply graphical methods to the solution of two engineering problems Task 3 involving exponential growth and decay, analysing the solutions using calculus (D2) Task 3.1 The voltage across the plates of a charging capacitor varies with time according to the formula v = 10 (1 - e-0.25t) Where t is the time in seconds (a) Using graph paper draw a graph showing the change in voltage in the first 15 seconds (b) Use the graph to estimate that rate at which the voltage is rising after 2.7 s (c) Use calculus to calculate the rate at which the voltage is rising after 2.7 s Task 3.2 The voltage across the plates of a capacitor at any time (t seconds) is given by v = Ve where V, C and R are constants. Given maximum voltage (V) = 10 volts, capacitance (C) = 0.20 10-6 farads and resistance (R) = 7 x 106 ohms; Using graph paper, (a) Draw a graph showing the change in voltage in the first 6 second (b) Use the graph to estimate the rate at which the voltage is initially decreasing. Indicate your workings on the graph. (c) Use calculus to calculate the rate at which the voltage is initially decreasing.