Question 383508
I am stuck on this question. The formula {{{"f(x)"=2x^2+22x+320}}} models the number of inmates(in thousands) in US State and federal prisons x years after 1980.
A) In which year were there 740 thousand inmates in US state and federal prisons?
<pre>
x = the number of years after 1980.

f(x) = the number of thoiusands of inmates in the year which is x years after 1980
</pre>
A) In which year were there 740 thousand inmates in US state and federal prisons?
<pre>
x = the number of years after 1980 = ?  (That's what we want to find)

f(x) = the number of inmates in the year which is x years after 1980 = 740  (That is given)

So we substitute 740 for f(x) in 

{{{"f(x)"=2x^2+22x+320}}}

{{{740=2x^2+22x+320}}}

Can you solve that? If not post again asking how.

Solutions are x = 10 and x = -21

We ignore the negative value and our final answer is

10 years after 1980, or the year 1990.
</pre>
B) In which year where there 1100 thousand inmates in US state and federal prisons?
<pre>

x = the number of years after 1980 = ? (That's what we want to find)

f(x) = the number of inmates in the year which is x years after 1980 = 1100  (That is given)

So we substitute 1100 for f(x) in 

{{{"f(x)"=2x^2+22x+320}}}

{{{1100=2x^2+22x+320}}}

Can you solve that? If not post again asking how.

Solutions are x = 15 and x = -26

We ignore the negative value and our final answer is

15 years after 1980, or the year 1995.

Edwin</pre>