1 a On January 1 2017 the world population was 7362350168 an

1.)

a.) On January 1, 2017, the world population was 7,362,350,168 and is growing at 1.05% per year. Create a formula for the world population as a function of time since 2017, then predict the world population for 2050.

b.) Currently there is about 7.68 billion acres of arable land, however, it is reducing by 24 million per year. Create a formula for the acres of arable land as a function of the time since 2017. Use this formula to predict how much arable land there will be in 2050.

c.) Calculate how much arable land there will be per person in 2050.

d.) It is estimated that we need 1 arable acre per person in order to have enough food. When will there be less than 1 acre of arable land per person?

Solution

Population on Jan 1st 2017 = 7,362,350,168
Year on Year growth = 1.05 %;
Thus population after \'x\' years from 2017 = 7,362,350,168 * (1.0105)^x;
For population in 2050, x= 2050-2017 = 33; Thus population in 2050 = 7,362,350,168 * (1.0105)³³; = 10,392,378,568;
Hence population in 2050 (predicted) = 10,392,378,568;

b) In 2017 there is 7.68 billion acres of arable land or 7680 million acres; Each year 24 million acres is reducing;
So after \'y\' years from 2017, the total arable land will be = (7680-24y) million acres;
Thus in 2050, y= 2050-2017 = 33; so total area of arable land left = (7680-24*33) = 7680-792 = 6888 million acres;

c) total arable land per person in 2050 = 6888 million / 10,392,378,568 = 0.662793 acres;
Thus, total arablel and per person in 2050 = 0.662793 acrs;
d) for arable land per person to go less than 1 acre:
7,362,350,168 * (1.0105)^x / (7680-24x) 10⁶ =1 (since currently in 2017 it is >1 we will consider =1 as the tipping off point)

7362350168 (1.0105)^x = (7680-24x) 10⁶
Solving for \'x\' you get x=4;
implies 2017+4 = 2021 is the year ;
In 2021, there will be less than 1 acre of arable land per person;