Question

A scientist counts 50 bacteria present in a culture and finds that the number of the bacteria in the culture doubles each hour. What is the function that models the number of bacteria after x hours?

Answer 1

50*(2^x) i think
cause if its the first hour it would be 50*2, then (50*2)*2, then ((50*2)*2)*2
so basically 50*2^3 and so on... :)

Answer 2

Yes, you can write a doubling equation like this as \[P(t) = P_0*2^t\]where \[P(0) = P_0\]

Sometimes you'll see it written as \[P(t) = P_0 e^{\lambda t}\]where \[\lambda = \frac{\ln 2}{t_2} \]and \(t_2\) is the time it takes to double.