0 14 40 40r 30. 30 20 20 10 2 4 61012 10 12 40F 15 30 20 Solution Dear student T

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Dear student Thank you for using chegg !! Given B = 50 + 7t - 30 e^0.1t a) Plot B Now at t = 0 B = 50 + 0 - 30 (1) => B = 20 Hence the required curve can be either A, B or C but not option D ( since in option D, B=0 at t =0) At t=1 B = 50 + 7 - 30 e^0.1 23.84487246 => the value of B is increasing from t=0 to t=1 Hence option A & option C are also not possible. since here curve is decreasing from t=0 to t=1 Correct opton is option B b) At what time B s at its max value To determine maxima position dfferenciate B w.r.t t dB/dt = 7 - 3e^0.1t Now dB/dt =0 when 7 - 3 e^0.1t = 0 e^0.1t = 7 / 3 Tanking natural log both sides 0.1t = 0.84729786 t = 8.472978604 => t = 8.47 So it will hit maximum at t = 8.47 years c) Value of B at t = 12 is given by B = 50 + 7t - 30 e^0.1t = 50 + 7 (12) - 30 e^(0.1*12) 34.39649232 Clearly the value of B was 20 at t =0, it grew to maxima at t=8.47 ( B = aroubnd 39) and then starts descending as is clear from value at t= 12. Therefore minimum value from t=0 to t= 12 is B = 20 Solution

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