Question: Various models have been used to make projections of growing populations. Thomas Malthus made one of the most famous conjectures of such a model in the early 19th century. Within Malthus’ claim was that the population of Earth would inevitably outstrip its means of a food supply. Records indicate that in 1950, the world’s population was about 2.5 billion people and was growing at a rate of about 2% per year. Also, in 1950, the world’s occupants had the ability to produce enough food for about 5 billion people annually and this food production was growing at about 250 million people per year. Given these data, could Malthus’ claim be correct?

Question

Question: Various models have been used to make projections of growing populations. Thomas Malthus made one of the most famous conjectures of such a model in the early 19th century. Within Malthus’ claim was that the population of Earth would inevitably outstrip its means of a food supply. Records indicate that in 1950, the world’s population was about 2.5 billion people and was growing at a rate of about 2% per year. Also, in 1950, the world’s occupants had the ability to produce enough food for about 5 billion people annually and this food production was growing at about 250 million people per year. Given these data, could Malthus’ claim be correct?

soooo im pretty sure that i need to use the equation… A=P(1+r)^t But how do i solve it from here?

Answer 1

To determine whether Malthus' claim could be correct, we can use the equation A = P(1 + r)^t, where A is the future population, P is the initial population, r is the growth rate, and t is the time period.

Let's plug in the given data:

Initial population (P) = 2.5 billion people
Growth rate (r) = 2% per year (0.02)
Time period (t) = ?

To find the time period, we need to know the future population (A). In this case, the future population is not explicitly given, but we can calculate it based on the information about food production.

It is stated that in 1950, the world's occupants had the ability to produce enough food for about 5 billion people annually, and food production was growing at about 250 million people per year.

Let's assume that the food production rate remains constant over time, and that it is directly proportional to the population growth rate. In other words, for every 1% increase in population, food production increases by 50 million people per year. So, if the population grows by 2%, food production would increase by 2 * 50 million = 100 million people per year.

Now, let's calculate the future population:

Food production growth rate = 100 million people per year
Difference between food production and initial food supply = 5 billion - 2.5 billion = 2.5 billion people

To find the time period (t), we can use the equation:

Difference between food production and initial food supply = Food production growth rate * t

2.5 billion = 100 million * t

Dividing both sides by 100 million:

2.5 billion / 100 million = t

t = 25

Therefore, the time period (t) is 25 years.

Now we have all the information to calculate the future population (A):

A = P(1 + r)^t
A = 2.5 billion * (1 + 0.02)^25

Calculating this, we find that the future population (A) is approximately 5.45 billion people.

Since the estimated future population of 5.45 billion is less than the estimated food production capacity of 5 billion, Malthus' claim that the population of Earth would outstrip its means of food supply does not hold based on these projections.

Answer 2

To determine whether Malthus' claim that the population of Earth would outstrip its means of food supply is correct, we need to compare the growth rate of the population to the growth rate of food production.

The equation you mentioned, A = P(1+r)^t, can be used to calculate the future population (A) based on the current population (P), the growth rate (r), and the time period (t). However, in this case, we want to use it to find out if the population growth will exceed the food production.

Let's start by plugging in the given data into the equation:

P = 2.5 billion (initial population in 1950)
r = 2% (annual growth rate)
t = number of years

Now, we need to find the value of t where the population exceeds the food production. So, we want to determine when A (population) becomes greater than 5 billion (food production).

Let's set up the equation:

A = 5 billion
2.5 billion(1+0.02)^t > 5 billion

Now, we can solve for t. Here's how:

1. Divide both sides of the equation by 2.5 billion:
(1+0.02)^t > 2

2. Take the natural logarithm (ln) of both sides of the equation:
ln((1+0.02)^t) > ln(2)

3. Use the property of logarithms to bring the exponent down:
t * ln(1+0.02) > ln(2)

4. Divide both sides of the equation by ln(1+0.02):
t > ln(2) / ln(1.02)

Using a calculator to compute ln(2) ≈ 0.693 and ln(1.02) ≈ 0.019, we can calculate:

t > 0.693 / 0.019
t > 36.47

So, the population will exceed the food production after approximately 36.47 years.

Considering that the data is from 1950, adding 36.47 years would give us 1986.47. Therefore, by the year 1987, Malthus' claim would suggest that the population would have outstripped its means of food supply.

It's important to note that this analysis is based on the given data and the assumption that the growth rates remain constant. In reality, population growth and food production rates may vary over time due to various factors.