Question

The number of incarcerated adults N​ (measured in​ thousands) in a certain country can be approximated by the equation Upper N equals negative 2.7 x squared plus 72.4 x plus 1911​, where x is the number of years since 2000. In 2013​, the number of incarcerated adults peaked. How many adults were incarcerated in that​ year?

Answer 1

2,396,000 adults were incarcerated in 2013.

Explanation:

The number of incarcerated adults N​ (measured in​ thousands) in a certain country can be approximated by the equation

N = -2.7x² + 72.4x + 1911

where x is the number of years since 2000.

In 2013, x = 2013 - 2000 = 13, and the number of incarcerated adults was

N = -2.7(13)² + 72.4(13) + 1911

N = -456.3 + 941.2 + 1911

N = 2,396

2,396 thousands (2,396,000) adults were incarcerated in 2013.

Answer 2

3308.5 thousands or 3,308,500.

Explanation:

We have been given a formula that represented the number of incarcerated adults N​ (measured in​ thousands) in a certain country can be approximated by the equation
`N=2.7x^2+72.4x+1911` where x is the number of years since 2000.

To find the number of incarcerated adults in 2013, we will substitute
`x=13`
`(2013-2000=13)` in the given equation.

`N=2.7(13)^2+72.4(13)+1911`

`N=2.7*169+941.2+1911`

`N=456.3+941.2+1911`

`N=3308.5`

Since the number of incarcerated adults N​ is measured in​ thousands, so the value of N would be:

`3308.5\text{ thousands}=3308.5* 1,000`

`3308.5\text{ thousands}=3,308,500`

Therefore, 3,308,500 adults were incarcerated in 2013.