Question

A student looking at global population figures remarks that between the years 1950 and 2010 the global population can be modelled by the equation 300y = 23t − 44 180 (1950 ≤ t ≤ 2010) Using algebra, calculate the year in which the population passed 6 billion

Answer 1

The year in which the population passed 6 billion is 2000.

Explanation:

We are given that a student looking at global population figures remarks that between the years 1950 and 2010 the global population can be modeled by the equation 300y = 23t − 44180; where (1950 ≤ t ≤ 2010).

And we have to calculate the year in which the population passed 6 billion.

The given expression is;

`300y=23t-44180`

Firstly, put t = 1960 {as t lies between 1950 and 2010}

`300y=(23* 1960)-44180`

`300y=45080-44180`

`300y=900`

`y = (900)/(300)` = 3 billion

But we have to cross the population by 6 billion.

Now, put t = 1999 in the expression;

`300y=(23* 1999)-44180`

`300y=45977-44180`

`300y=1797`

`y = (1797)/(300)` = 5.99 billion

Still, it's not passed 6 billion, so finally put t = 2000;

`300y=(23* 2000)-44180`

`300y=46000-44180`

`300y=1820`

`y = (1820)/(300)` = 6.1 billion

Now, the global population has crossed 6 billion.

Hence, the year in which the population passed 6 billion is 2000.