Question

beginning with the year 2010, an agency projected how the assets of the fund were going to change through the year 2035. the projection of assets can be modeled by the function a(x)= - 0.009x² + 0.127x + 2.372, where a(x) represents the amount of assets in trillions of dollars x years after 2010. x = 0 corresponds to the year 2010, x = 5 corresponds to the year 2015, etc. complete parts a through e.
a. complete the following table using your calculator.
(round to three decimal places as needed.)
x, number of years since 2010 0 5 10 15 20
a(x), assets in trillions of dollars 2.372 2.782 2.742 2.252 1.312
b. evaluate a(11) and explain its meaning in this situation.
a(11)= 2.680 trillion dollars (round to three decimal places as needed.)
explain the meaning of a(11) in this situation. select the correct choice below and fill in the answer box to complete your choice.
○ a. the model predicts that the fund will have assets of 11 trillion dollars in
(round to the nearest year as needed.)
○ b. the model predicts that the fund will have assets of trillion dollars in
(round to three decimal places as needed. round to the nearest year as needed.)

Explanation:

Step1: Recall the function

The function for the assets is $A(x)= - 0.009x^{2}+0.127x + 2.372$.

Step2: Substitute $x = 11$

We substitute $x = 11$ into the function:
\[

$$\begin{align*} A(11)&=-0.009\times(11)^{2}+0.127\times11 + 2.372\\ &=-0.009\times121 + 1.397+2.372\\ &=-1.089+1.397 + 2.372\\ &=2.680 \end{align*}$$

\]
Since $x$ represents the number of years after 2010, when $x = 11$, it corresponds to the year $2010 + 11=2021$.

Answer:

B. The model predicts that the fund will have assets of $2.680$ trillion dollars in 2021.