In 1990, approximately 1,820,000 violent crimes were reported in the U. S. By 2019, this number had fallen to approximately 1,200,000. (a) Write a linear model to describe the number of violent crimes in the U. S. from 1990 onward.

Pt =

(b) Using this linear model, predict the number of violent crimes in 2032. Round your answer to the nearest whole number.

violent crimes

(c) When do you expect the number of violent crimes to reach 800,000? Give your answer as a calendar year (ex: 2020).

During the year

$11.60 is your answer but this is in us dollars

is continuous on its domain of .

is continuous from the left at -1 and continuous from the right at 1.

assuming domain and codomain of all real numbers, function is only defined for nonnegative radicands:

there are many ways of solving a quadratic inequality. here we will reason by cases, using the definition of absolute value.

if then and so the inequality turns into when x ≥ 0. of course, "x≥3 when x≥0" simplifies to x ≥ 3.

or, if , then and so when . of course, "x≤-3 when x < 0" simplifies to x ≤ -3.

so the domain of is

now, is a continuous function since it is a composition of continuous functions. is a polynomial and (the parent) is a root function; both of them are continuous on their domains. therefore, is continuous on its domain of .

by definition, a function is continuous from the left at a number a if and continuous from the right at a number a if .

checking continuity at the end points, note that

and

so is continuous from the left at -1 and continuous from the right at 1.