Find and expression that gives dictation speed

label Calculus
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Jul 23rd, 2015

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N'(t) = 4e^(−0.05t)        (0 ≤ t ≤ 20)
  intergrating we get N =  4[1/(- 0.05)] e^(−0.05t) + C ;  or we can write  N = - 80 e^(−0.05t) + C
at t = 0, N = 75  therefore  75 = - 80 e^[(- 0.05)(0)] + C
C = 155
hence     N(t) =  155 - 80 e^(−0.05t)    for (0 ≤ t ≤ 20)

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Jul 23rd, 2015

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