Q1 The current population of Tanzania is 49.3 million with a population growth r

Question

Q1

The current population of Tanzania is 49.3 million with a population growth rate of 2.93% per year. The average annual agricultural yield in Tanzania is 8500 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 4,000,000 ha. The average agricultural output has increased at a linear rate of about 1.5% 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.

Using what you know about exponential growth as we've described it, what would you predict the population of Tanzania to be 6.4 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.

Q2

The current population of Tanzania is 49.3 million with a population growth rate of 2.93% per year. The average annual agricultural yield in Tanzania is 8500 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 4,000,000 ha. The average agricultural output has increased at a linear rate of about 1.5% 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.

Using what you know about exponential growth as we've described it, what would you predict the population of Tanzania was 5.9 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 then your answer is 33.4 Million and you would enter 33.4 as your answer.

QUESTION 3

The current population of Tanzania is 49.3 million with a population growth rate of 2.93% per year. The average annual agricultural yield in Tanzania is 8500 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 4,000,000 ha. The average agricultural output has increased at a linear rate of about 1.5% 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.

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.

QUESTION 4

The current population of Tanzania is 49.3 million with a population growth rate of 2.93% per year. The average annual agricultural yield in Tanzania is 8,849 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 3,819,331 ha. The average agricultural output has increased at a linear rate of about 1.5% 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.

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? Again, round your answer to one place past the decimal and put your answer in "millions", so that if your answer is 155,870,000 your answer is 155.9 Million and you would enter 155.9 as your answer. 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.

QUESTION 5

The current population of Tanzania is 49.3 million with a population growth rate of 2.14% per year. The average annual agricultural yield in Tanzania is 8950 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 4,500,000 ha. The average agricultural output has increased at a linear rate of about 1.04% 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.

If Tanzania can currently feed 110 Million people, in what year will they 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. The current year is 2,015.

Explanation / Answer

1) Given P0 = 49.3 million

Rate of population growth r = 2.93% per year

Population of Tanzania 6.4 years from now P6.4 = P0(1+r/100)6.4 = 49.3(1+2.93/100)6.4 = 59.3 Millions.

Hence the answer is 59.3

2) Let the population of Tanzania 5.9 years ago be P.

49.3 = P(1+2.93/100)5.9

Thus P= 41.6 Millions. Hence answer is 49.6

3) Let the no. of years required for Tanzania's population to double be n

2*49.3 = 49.3(1+2.93/100)n

Hence n = 24.0 years

4) Given average annual agricultural yield = 8849kg/ha

Amount of cropland farmed in Tanzania = 3819331 ha

Hence the average annual agricultural yield = 8849*3819331 = 33.8*109kg

Since the agricultural output increases linearly at the rate of 1.5% per year for the last five years.

But as obtained from the last question Tanzania is self sufficient for 38 years from the current year hence rate of increase factor will not apply as it applies only to the last five years.

Both grains and tubers are produced in a 1:1 ratio.

Hence the amount of grains produced = amount of tubers produced = 33.8*109/2 = 16.9*109kg

Given 1kg grain supplies 3000 Kcal and 1kg tuber supplies 1000 Kcal

Hence total energy produced by grains = 16.9*109*3000 = 50.7*1012 Kcal

Total energy produced by tubers = 16.9*109*1000= 16.9*1012 Kcal

Calorific intake of a person to sustain life = 2000Kcal per day

Hence calorific intake of a person in an year = 2000*365 = 7.3*105kcal

Hence the no. of people Tanzania can currently feed = (50.7*1012+16.9*1012)/7.3*105 =92.6 Millions

Hence answer is 92.6

5)Given average annual agricultural yield = 8950 kg/ha

Amount of cropland farmed in Tanzania = 4500000 ha

Hence the average annual agricultural yield = 8950*4500000 = 40.3*109kg

Since the agricultural output increases linearly at the rate of 1.04% per year for the last five years.

Hence the current agricultural output = 40.3*109*1.0104 = 40.72*109kg

Both grains and tubers are produced in a 1:1 ratio.

Hence the amount of grains produced = amount of tubers produced = 40.72*109/2 = 20.36*109kg

Given 1kg grain supplies 3000 Kcal and 1kg tuber supplies 1000 Kcal

Hence total energy produced by grains = 20.36*109*3000 = 61.08*1012Kcal

Total energy produced by tubers = 20.36*109*1000 = 20.36*1012kcal

Calorific intake of a person to sustain life = 2000Kcal per day

Hence calorific intake of a person in an year = 2000*365 = 7.3*105kcal

Hence the no. of people Tanzania can feed before starting importing food = (61.08*1012+20.36*1012)/7.3*105 = 111.56 Millions

Current population = 49.3 Million

Let n be the no. of years for which Tanzania is self sufficient in terms of food. Tanzania will be sufficient only if its population does not exceed the population it can feed

111.56 =49.3(1+2.14/100)n

Thus n =38.6 years

Thus the year till which Tanzania will be self sufficient in terms of food = 2015+38 = 2053.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.