Help Calculus Problem

label Calculus
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schedule 1 Day
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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!

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


N = 250/ln3*(3^2.4-1)+100 = 3951


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

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