Question

A colony of bacteria is growing exponentially, doubling in size every 50 minutes, How many minutes will it take for the colony to become six times it current size?

Answer 1

Do you know the formula for doubling growth rate?

Answer 2

the exponential growth and doubling equation is:
P(t)=Po(2)^(t-to)/d

Answer 3

\[6=2^{\frac{t}{50}}\] solve for \(t\)

Answer 4

takes exactly two steps:
change of base gives
\[\frac{t}{50}=\frac{\ln(6)}{\ln(2)}\]
\[t=\frac{50\ln(6)}{\ln(2)}\]

Answer 5

what would the exact answer be and how would you solve that, i want to understand each step.