Please help with calculus question!

label Calculus
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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.

Jul 22nd, 2015

Thank you for the opportunity to help you with your question!

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 


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 22nd, 2015

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