The proportion P of doctors aware of a new treatment after t months may be modeled by the differential equation dP/dt = k(0.9-P) where k is a constant.
(a) Write the first-order linear differential equation in standard form.
(b) Solve for P(t ) given that P(0) = 0
(c) Suppose that for P(6) = 0.5 . Use this to determine k.
(d) Find P(18).
(e) Find t so that P(t ) = 0.85 . In other words, how many months will it take for 85% of doctors to become aware of this treatment?
(a) P? + kP = 0.9k
(b) 
(c) 0.135155
(d) 0.82
(e) 21.39 or ~22 months
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? 
A. 
B. 
C. 
D. 
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A. g(x) = 
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D. g(x) = 1/8, h(x) = x2 - 8
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- 15 ln 
A. ln 
B. ln(x3 - y12)
C. ln 
D. ln 