Question

If the populATION of bacteria doubles every 30 minutes, how long would it take for the population to triple?

(question from logarithms homework)

Answer 1

x=0,y=1;x=30,y=2,so \[y=(\sqrt[30]{2})^x\]
when y=3,solve for x:\[3=(\sqrt[30]{2})^x\]
\[x=\log_{\sqrt[30]{2}}3 \]

Answer 2

ok or try
\[3=2^{\frac{t}{30}}\] solve for t

Answer 3

\[x=30*\log_{2} 3\]

Answer 4

solve via
\[\ln(3)=\frac{t}{30}\ln(2)\]

\[\frac{t}{30}=\frac{\ln(3)}{\ln(2)}\]
\[t=30\frac{\ln(3)}{\ln(2)}\]

Answer 5

same answer as jwt but this one you can find the number on a calculator.

Answer 6

i get 47.55 rounded so between day 47 and 48

Answer 7

between 47and48 minutes