Description
Under certain conditions, the number of cancer cells N(t) at time( t) increases at a rate of N'(t) =50e^kt . Suppose that at 5 days, the number of cells is growing at a rate of 150 cells per day. Determine a number of cells after 12 days if there were 100 cells initially.
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N' = dN/dt = 50 e^kt
N = 50/k e^kt +c
t = 0 N = 100
c = 100-50/k
t = 5, N' = 50 e^5k = 150
e^5k = 3
k = 1/5 ln3 = 0.2197
c = 100-50/k = -127.56
N = 227.56*e^(0.2197t) -127.56
t =12
N = 227.56 *e^2.6364 - 127.56 =3077
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