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The number of U.S. travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function

[tex]\[ P(x) = -0.00880x^3 + 0.1467x^2 + 1.286x + 42.87 \][/tex]

where [tex]\( x = 0 \)[/tex] represents 1990, [tex]\( x = 1 \)[/tex] represents 1991, and so on. [tex]\( P(x) \)[/tex] is in millions. Use this function to approximate the number of U.S. travelers to other countries in parts (a) through (c).

(a) Approximate the number of U.S. travelers to other countries in 1990.

In 1990, the number of U.S. travelers to other countries was approximately [tex]\(\boxed{\phantom{0}}\)[/tex] million.



Answer :

GinnyAnswer
To find the number of U.S. travelers to other countries in 1990 using the given polynomial function [tex]\( P(x) = -0.00880x^3 + 0.1467x^2 + 1.286x + 42.87 \)[/tex], we need to determine [tex]\( P(x) \)[/tex] when [tex]\( x = 0 \)[/tex].

Since [tex]\( x = 0 \)[/tex] represents the year 1990, we can substitute [tex]\( x = 0 \)[/tex] into the polynomial:

[tex]\[ P(0) = -0.00880(0)^3 + 0.1467(0)^2 + 1.286(0) + 42.87 \][/tex]

From the terms involving [tex]\( x \)[/tex]:

- [tex]\(-0.00880(0)^3 = 0\)[/tex]
- [tex]\(0.1467(0)^2 = 0\)[/tex]
- [tex]\(1.286(0) = 0\)[/tex]

So, we have:
[tex]\[ P(0) = 0 + 0 + 0 + 42.87 \][/tex]
[tex]\[ P(0) = 42.87 \][/tex]

Therefore, the number of U.S. travelers to other countries in 1990 was approximately [tex]\( 42.87 \)[/tex] million.

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