How do I find the rate "R" variable in this exponential growth model?

Question

The area covered by a certain population of bacteria increases according to a continuous exponential growth model . Suppose that a sample culture has an initial area 54.6mm^2 of and an observed doubling time of 23 hours. I need to make this into a Y=Pe^rt expression, but I dont know how I should find the RATE "R" for this. It says "Doubling time of 23 hours", but how do i write this as a RATE in the equation?

Answer 1

y = Pe^rt

 

Doubling time is 23 hours, so when t = 23, y = 2P:

 

y = Pe^rt

2P = Pe^23r

2 = e^23r

ln(2) = 23r

ln(2)/23 = r