I did this problem already but want to make sure my steps are correct, please show all work/explanations

1)

a) the amount of dogs born will increase from 35.6 million in 2000 to 102.6 million in 2050

.unlimited growth model dy/dt = ky fits this population growth

.express the population y as a function of the year t

Let 2000 correspond to t = 0.

b) Assume instead that the population will grow according to a limited growth model where the carrying capacity is N = 800 million , K=2

.Write down the differential equation for the limited growth equation

.express the population y as a function of the year t.