Question

calc 2
how to solve the number of cells in a tumor doubles every 6 weeks starting with 8 cells. after how many weeks does the tumor have 1500 cells?
ans 45.3 weeks

Answer 1

week 0 -> 8
week 6 -> 8*2
week 12 -> 8*2^2
and so on
week n -> \(8\times2^{n/6}\)
so, we have a general formula
\[
N(n)=8\times2^{n/6}\\
\implies1500=8\times2^{n/6}\\
\implies187.5=2^{n/6}\\
\implies\ln(187.5)={n\over6}\ln(2)\\
\implies n=6\times{\ln(187.5\over\ln(2)}\\
\implies\boxed{n=45.3}
\]