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the number of us travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function

the number of us travelers to other countries during the period from 1990 through-example-1
User Msanders
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1 Answer

5 votes

SOLUTION

We want to use the model below to solve the question

(a) Since x = 0 represents 1990, the number of travelers in 1990 becomes


\begin{gathered} We\text{ will put } \\ x=0,\text{ into the function } \\ P(x)=-0.00690x^3+0.1190x^2+1.361x+44.82 \end{gathered}

We have


\begin{gathered} P(0)=-0.00690(0)^3+0.1190(0)^2+1.361(0)+44.82 \\ =0+0+0+44.82 \\ =44.82 \end{gathered}

Hence the answer is 44.8 million to the nearest tenth

(b) 2000. From 1990 to 2000 is 10 years. So, we will substitute 10 for x into the function, we have


\begin{gathered} P(x)=-0.00690x^3+0.1190x^2+1.361x+44.82 \\ P(10)=-0.00690(10)^3+0.1190(10)^2+1.361(10)+44.82 \\ P(10)=-0.00690(1000)+0.1190(100)^{}+13.61+44.82 \\ P(10)=-6.90+11.90^{}+13.61+44.82 \\ =63.43 \end{gathered}

Hence the answer is 63.4 million to the nearest tenth

(c) From 1990 to 2009 is 19 years. Substituting 19 for x, we have


\begin{gathered} P(x)=-0.00690x^3+0.1190x^2+1.361x+44.82 \\ P(19)=-0.00690(19)^3+0.1190(19)^2+1.361(19)+44.82 \\ P(19)=-0.00690(6,859)^{}+0.1190(361)^{}+25.859+44.82 \\ P(19)=-47.3271^{}+42.959^{}+25.859+44.82 \\ =66.3109 \end{gathered}

Hence the answer is 66.3 to the nearest tenth

the number of us travelers to other countries during the period from 1990 through-example-1
User Alfoks
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