The number of U. S. travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function Upper P (x )equals negative 0.00680 x cubed plus 0.1018 x squared plus 1.458 x plus 48.09 where xequals0 represents 1990, xequals1 represents 1991, and so on and P(x) is in millions. Use this function to approximate the number of U. S. travelers to other countries in each given year. (a) 1990 (b) 2000 (c) 2009

a) 48.09 million

b) 56.888 million

c) 31.085 million

Step-by-step explanation:

We are given the following in the question:

where P(x) in millions is the number of U.S. travelers from 1990 through 2009 and x = 1 represents 1991.

We have to approximate the number of U.S. travelers to other countries in each given year.

(a) 1990

We put x = 0 in the given function.

Thus, there are 48.09 millions U.S. travelers in 1990.

(b) 2000

We put x = 10 in the given function.

Thus, there are 56.888 millions U.S. travelers in 2000.

(c) 2009

We put x = 19 in the given function.

Thus, there are 31.085 millions U.S. travelers in 2009.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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