Write your answer as a percentage. Do not round any intermediate computations, and round your answer to the nearest hundredth

Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1900 bacteria selected from this population reached the size of 1998 bacteria in one and a half hours. Find the hourly growth rate parameter. 

Answer 1

f(t) = P*exp(k*t)

 

 

1900  = f(0) = P  <--- initial population at time zero

 

f(t) = 1900*exp(k*t)

 

 

1998 = 1900*exp(1.5*t)

 

1998/1900 = exp(1.5t)

 

ln(1998/1900) = 1.5*t

 

t  = 1n(1998/1900)/1.5

 

t = 0.03352853