Im solving the following problem:

The population of the world was about 6.3 billion in 2000. Birth rates around that time ranged from 35 to 40million per year and death rates ranged from 15 to 20 million per year. Assume the carrying capacity of theworld is 100 billion people.

(a) Write a logistic differential equation for these data. (Use the fact since the population is small comparedto the carrying capacity that you can take k to be an estimate of the relative growth rate.)

How is that given the rates of birth and death we can estimate the relative growth rate k?

I'm confused about the logic behind getting our relative growth rate.