Question

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

Answer 1

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