A population of rabbits in a certain habitat grows according to the differential equation / = 0.4( + 1)

where is measured in months ( 0) and is measured in hundreds of rabbits.

There were initially 100 rabbits in this habitat.

a) What is the initial condition in this problem as it relates to the mathematical equation?

b) Write a sentence describing the rate that the population of rabbits is changing when there are 500 rabbits in the habitat.

c) Find a particular solution to this differential equation.

d) Use your equation from c) to determine how many rabbits will be at the habitat one year after the initial formation of said habitat.