Questions: The assets (in billions of dollars) for a financial firm can be approximated by the function A(x)=330 e^.056 x, where x=7 corresponds to the year 2007. Find the assets in each of the following years. (a) 2011 (b) 2014 (c) 2017 (a) Which of the following describes how to find the assets in 2011 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2011, substitute for x and evaluate to find A(x). B. To find the assets in 2011, find the intersection point of the graphs y=330 e^.056 x and y=. The assets in 2011 are represented by the y-coordinate. In 2011 the assets are about billion. (Type an integer or decimal rounded to the nearest tenth as needed.) (b) Which of the following describes how to find the assets in 2014 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2014, find the intersection point of the graphs y=330 e^.056 x and y=. The assets in 2014 are represented by the y-coordinate. B. To find the assets in 2014, substitute for x and evaluate to find A(x). In 2014 the assets are about billion. (Type an integer or decimal rounded to the nearest tenth as needed.) (c) Which of the following describes how to find the assets in 2017 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2017, substitute for x and evaluate to find A(x). B. To find the assets in 2017, find the intersection point of the graphs y=330 e^.056 x and y=. The assets in 2017 are represented by the y-coordinate.

The assets (in billions of dollars) for a financial firm can be approximated by the function A(x)=330 e^.056 x, where x=7 corresponds to the year 2007. Find the assets in each of the following years. (a) 2011 (b) 2014 (c) 2017 (a) Which of the following describes how to find the assets in 2011 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2011, substitute for x and evaluate to find A(x). B. To find the assets in 2011, find the intersection point of the graphs y=330 e^.056 x and y=. The assets in 2011 are represented by the y-coordinate. In 2011 the assets are about billion. (Type an integer or decimal rounded to the nearest tenth as needed.) (b) Which of the following describes how to find the assets in 2014 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2014, find the intersection point of the graphs y=330 e^.056 x and y=. The assets in 2014 are represented by the y-coordinate. B. To find the assets in 2014, substitute for x and evaluate to find A(x). In 2014 the assets are about billion. (Type an integer or decimal rounded to the nearest tenth as needed.) (c) Which of the following describes how to find the assets in 2017 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2017, substitute for x and evaluate to find A(x). B. To find the assets in 2017, find the intersection point of the graphs y=330 e^.056 x and y=. The assets in 2017 are represented by the y-coordinate.
Transcript text: The assets (in billions of dollars) for a financial firm can be approximated by the function $\mathrm{A}(\mathrm{x})=330 e^{.056 \mathrm{x}}$, where $\mathrm{x}=7$ corresponds to the year 2007. Find the assets in each of the following years. (a) 2011 (b) 2014 (c) 2017 (a) Which of the following describes how to find the assets in 2011 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2011, substitute $\square$ for $x$ and evaluate to find $A(x)$. B. To find the assets in 2011, find the intersection point of the graphs $\mathrm{y}=330 e^{.056 \mathrm{x}}$ and $\mathrm{y}=$ $\square$ . The assets in 2011 are represented by the $y$-coordinate. In 2011 the assets are about \$ $\square$ billion. (Type an integer or decimal rounded to the nearest tenth as needed.) (b) Which of the following describes how to find the assets in 2014 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2014, find the intersection point of the graphs $\mathrm{y}=330 e^{.056 \mathrm{x}}$ and $\mathrm{y}=$ $\square$ . The assets in 2014 are represented by the $y$-coordinate. B. To find the assets in 2014 , substitute $\square$ for $x$ and evaluate to find $A(x)$. In 2014 the assets are about \$ $\square$ billion. (Type an integer or decimal rounded to the nearest tenth as needed.) (c) Which of the following describes how to find the assets in 2017 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the assets in 2017 , substitute $\square$ for $x$ and evaluate to find $A(x)$. B. To find the assets in 2017, find the intersection point of the graphs $\mathrm{y}=330 e^{.056 \mathrm{x}}$ and $\mathrm{y}=$ $\square$ . The assets in 2017 are represented by the $y$-coordinate.
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Solution

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Solution Steps

To find the assets for the given years, we need to substitute the corresponding value of \( x \) into the function \( A(x) = 330 e^{0.056x} \). The value of \( x \) is determined by the number of years since 2007. For example, for 2011, \( x = 4 \) because 2011 is 4 years after 2007. Similarly, calculate \( x \) for 2014 and 2017, and then evaluate the function for each year.

Step 1: Calculate Assets for 2011

To find the assets in 2011, we substitute \( x = 4 \) into the function \( A(x) = 330 e^{0.056x} \): \[ A(4) = 330 e^{0.056 \cdot 4} \approx 412.9 \] Thus, the assets in 2011 are approximately \$412.9 billion.

Step 2: Calculate Assets for 2014

Next, for 2014, we substitute \( x = 7 \) into the same function: \[ A(7) = 330 e^{0.056 \cdot 7} \approx 488.4 \] Therefore, the assets in 2014 are approximately \$488.4 billion.

Step 3: Calculate Assets for 2017

Finally, for 2017, we substitute \( x = 10 \): \[ A(10) = 330 e^{0.056 \cdot 10} \approx 577.7 \] Consequently, the assets in 2017 are approximately \$577.7 billion.

Final Answer

The assets for each year are as follows:

  • In 2011: \\(\boxed{412.9}\\)
  • In 2014: \\(\boxed{488.4}\\)
  • In 2017: \\(\boxed{577.7}\\)
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