Mars Population
In the course, "Information, Computing and the Future", Dr. Daniel Berleant notes that Mars and Earth have land masses of similar area[1].He then asks the following hypothetical question regarding the possible future population of Mars:
If we start with a colony of 100 people,
and the rate of population growth is 5% per year,
how many years will have elapsed
by the time the population reaches 10 billion (1 x 10^10)?
We begin the induction by writing:
the population at year 0 = 100 then
the population at year 1 = 100*(1+0.05)
the population at year 2 = 100*(1+0.05)(1+0.05)
Noting that each year composes an instance of (1+0.05) in the rhs product we observe the exponential and write:
To warm up, we test our function asking, "What the population will be in a decade of years?":
So it might seem that our colony is not off to that ambitious a start.
Exploring our function further, we look at how it behaves for different rates of growth from 0 percent per year to 10 percent per year. Scaling the rate by a factor of 1000 so we can see it, we have:
Getting back to the original question we want to know the year that the population reaches the peak p of 10 billion, so we solve the function for the year. Since the abbreviation landscape is unambiguous, we shorten the names:
Since the function grows so rapidly, we write some date utility functions:
Solutions
