Question

11 multiple choice 1 point the number of answer machines sold can be modeled by the function f(x) = -0.010789x³ + 0.2226x² + 0.311x - 0.75 where x is the number of years since 1980 and f(x) is the number of in millions. use this function to find the number of answer machines sold in 1986.

Explanation:

Step1: Determine the value of x

Since \( x \) is the number of years since 1980, for the year 1986, we calculate \( x = 1986 - 1980 = 6 \).

Step2: Substitute x = 6 into the function \( f(x) \)

We have the function \( f(x)= - 0.010789x^{3}+0.2226x^{2}+0.311x - 0.75 \). Substitute \( x = 6 \) into it:
First, calculate each term:

• For the \( x^{3} \) term: \( - 0.010789\times6^{3}=-0.010789\times216=- 2.330424 \)
• For the \( x^{2} \) term: \( 0.2226\times6^{2}=0.2226\times36 = 8.0136 \)
• For the \( x \) term: \( 0.311\times6 = 1.866 \)
• The constant term: \( - 0.75 \)

Then, sum up all the terms:
\( f(6)=-2.330424 + 8.0136+1.866 - 0.75 \)
\( f(6)=(-2.330424-0.75)+(8.0136 + 1.866) \)
\( f(6)=-3.080424+9.8796 \)
\( f(6)=6.799176 \)

Answer:

The number of answer machines sold in 1986 is approximately \( 6.80 \) million (rounded to two decimal places) or exactly \( 6.799176 \) million.