The NASA finally makes it to Mars and sends $10$ people there. Nobody has children during this period. Any pregnant women are sent back to earth to have children. However, the population grows at a rate of $1$ person every five years for the first $20$ years because of people sent up by rocket. A disaster occurs in year $20,$ in which all but $4$ people die. NASA decides that it is immoral to send any more people to Mars, with such a high risk; however, the $4$ people on Mars refuse to go back to earth, and decide to start their own civilization on Mars. They set a goal of $500$ people by the Martian year $500.$ However, they ask NASA to help make recommendations on population growth and food supply systems. As the biosystems modeler back on Earth, you must tell the community how many children to recommend that each female must have in order to grow the population to $500$ by the Martian year $500($that is the slogan, $500$ by $500).$ As with Earth, one out of every two children is a female. As a Biosystems Modeler, you also consider what would happen if the planet Mars was dangerous. Make recommendations for the possibility that $25\%,50\%,$ or $75\%$ of the people do not reach child bearing age. You will need to set up a loop with some complexities, but remember that biological modeling often ignores the genetic or reproduction variability and just considers the average. Set up an analytical equation as well as a for loop that is based on averages. Also, write a paragraph to the Martians and the NASA administrators, which also considers any bioethical issues that might arise and how the community should deal with them. Model the $500-$year period. Determine the number of children per female, and the growth coefficient. You can do this problem in Excel, but you must use Solver to find the recommended number of children per female; use a Solver in Python that determines the number of children per female and model the growth in graphs.