Problema Solution
The following formula models the number of prison inmates, P, in thousands, who are in U.S. prisons x years after 1980.
P = 2 x^2+22 x+318
A) Find an equation in the form ax^2 + bx + c = 0 that you can use to solve determine the first year in which the population of U.S. prisons was approximately 370 thousand people. Do not solve it yet.
Answer: The equation is
B) Now factor your equation to solve it and specifiy the first year in which the population of U.S. prisons was approximately 370 thousand people.
Answer: The population reached 370 thousand people in the year
Answer provided by our tutors
A) 2*x^2+22*x+318 = 370
2*x^2+22*x+318 - 370 = 0
2*x^2+22*x - 52 = 0 divide both sides by 2
x^2+11*x - 26 = 0
The equation is x^2+11*x - 26 = 0
B) x^2+11*x - 26 = 0
(x - 2)(x + 13) = 0
since the number of years can not be negative the solution is x = 2 years
The population reached 370 thousand people in the year 1982.
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