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.
Explanation & Answer
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dN/dt = 50 e^kt
N = 50/k e^kt +c
at t = 5 N' = 50 e^5k = 150
e^5k = 3
k = 1/5*ln3
N = 50/k e^kt +c = 250/ln3 *3^(t/5)+c
t =0 N= 100
100 = 250/ln3 +c
c = 100-250/ln3
N = 250/ln3(3^(t/5)-1)+100
t=12
N = 250/ln3*(3^2.4-1)+100 = 3951
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