P(t) is the population size at time t (measured in days)
P₀ is the initial population size
K is the carrying capacity of the environment
r is a constant representing population growth or decay

Using this model, answer the following question.

Compute the value of r required for an initial population of 53 to reach a size of 152 in 30 days if the carrying capacity is 200. Round your answer to the nearest thousandth.