Answer:
a) P' = P
where t is step of 6 months
b) 7.7 years
c)1064.67 rabbits/year
Step-by-step explanation:
The differential equation describing the population growth is

Where t is the range of 6 months, or half of a year.
P(t) would have the form of

where
is the initial population
After 6 month (t = 1), the population is doubled to 48



Therefore 
where t is step of 6 months
b. We can solve for t to get how long it takes to get to a population of 1,000,000:




So it would take 15.35 * 0.5 = 7.7 years to reach 1000000
c. 
We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48



Therefore, 
At the mid of the 3rd year, where t = 2.5, we can calculate P'
rabbits/year