The current population of Tanzania is 47.1 million with a population growth rate of 2.5% per year. The average annual agricultural yield in Tanzania is 10000 kg/ha (where "ha" means hectare, which you can think of as a metric acre), a yield that is comprised of both grains (e.g. maize/corn) and tubers (e.g. cassava root) in a 1:1 ratio. The total amount of cropland farmed in Tanzania is 4000000 ha. The average agricultural output has increased at a linear rate of about 1.3% per year for the last five years or so. Ideally, one person should have a caloric intake of at least 2000 kcal per day in order to maintain their life. 1 kg grain supplies 3000 kcal; 1 kg tubers supplies 1000 kcal. Use the equations from our mini-lecture and the linear growth equation from the last module's quantitative assignment, to answer the following questions. You will also have to do some conversions for which you won't find specific equations.
(a) Using what you know about exponential growth as we've described it, what would you predict the population of Tanzania to be 5 years from now? Round your answer to one place past the decimal and put your answer in "millions", so that if your answer is 55,670,000 your answer is 55.7 Million and you would enter 55.7 as your answer.
(b) Using what you know about exponential growth as we've described it, what would you predict the population of Tanzania was 5 years ago? Hint: think backwards in time and once again: round your answer to one place past the decimal and put your answer in "millions", so that if your answer is 33,420,000 your answer is 33.4 Million and you would enter 33.4 as your answer.
(c) How many years would you predict it would take for Tanzania's population to double? Hint: Think doubling time as we've described it in the Module 3 mini-lecture. Round your answer to one place past the decimal.
(d) Assuming that all of the people of Tanzania eat only grains and tubers and considering only domestic production (i.e. they do not import food), how many people can Tanzania currently feed? Hint: Start by finding the total energy that Tanzania produces from food in one year's time. Then use that number and the number of kcals that one person needs to survive in one year, to determine your answer.
(e) In what year will Tanzania cease to be self-sufficient in food? In other words, when will they need to begin importing food? Hint: Plot both (i) population growth and (ii) food growth on the same set of axes for a span of 100 years or so (a point every 10 years should be enough for you to make a determination). The point where the two lines cross is the point after which they would need to start importing food. A spreadsheet program such as Excel may help though you could simply plot them on paper. Alternatively, you could use your scientific graphing calculator (if you have one) to determine the answer