Question

Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation

10.0y − 4.55x = 581
where x is the number of years after 2000.

(a)
What is the projected population in 2028?
y =

(b)
In what year is the population predicted to be 67.2 million?

Answer 1

a) 70.84 million

b) 2020

Explanation:

Given equation:

`10.0y-4.55x = 581`

where:

• y is the population of the UK in millions.
• x is the number of years after 2000.

Part (a)

2028 is 28 years after 2000.

Therefore, to calculate the projected population in 2028, substitute x = 28 into the equation and solve for y:

`\begin{aligned}\implies 10.0y-4.55x &= 581\\10.0y-4.55(28) &= 581\\10.0y-127.4 &= 581\\10.0y&= 708.4\\y&= 70.84\end{aligned}`

Therefore, the projected population in 2028 is 70.84 million.

Part (b)

To calculate the number of years after 2000 when the population is predicted to be 67.2 million, substitute y = 67.2 into the equation and solve for x:

`\begin{aligned}\implies 10.0y-4.55x &= 581\\10.0-4.55x &= 581\\672-4.55x &= 581\\-4.55x &= -91\\x&=20\end{aligned}`

To calculate the year, add the found value of x to 2000:

`\implies \textsf{Year}=2000+20=2020`

Therefore, the population is predicted to be 67.2 million in the year 2020.