The assets​ (in billions of​ dollars) for a financial firm can be approximated by the function Upper A left parenthesis x right parenthesis equals 323 e Superscript . 067 x
​, 
where xequals
7 
corresponds to the year 2007. Find the assets in each of the following years.
A. To find the assets in 2011, substitute 11 for xx and evaluate to find A(x)A(x
n 2011
 
the assets are about ​$enter your response here
 
billion.
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

The function for the assets $ A(x) $ of the financial firm is given by:

\[
A(x) = 323 e^{0.067x}
\]

where $ x = 7 $ corresponds to the year 2007. To find the assets in the year 2011, we need to determine the value of $ x $ that corresponds to 2011.

Since $ x = 7 $ corresponds to 2007, we can calculate $ x $ for 2011 as follows:

\[
x = 11
\]

Now, substitute $ x = 11 $ into the function:

\[
A(11) = 323 e^{0.067 \cdot 11}
\]

Let's compute this value to find the assets in 2011.The assets of the financial firm in 2011 are approximately **$675.0 billion**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would the assets change by 2020 if the growth rate remained constant?
2. What is the percentage increase in assets from 2007 to 2011?
3. How would a change in the growth rate affect the assets by 2015?
4. Can we determine the growth rate if only given the initial and final assets over a period?
5. How would the model behave if the growth rate became negative?

**Tip:** Understanding exponential growth can help predict long-term trends in financial markets and investments.

The assets (in billions of dollars) for a financial firm can be approximated by the function A(x) = 323e^(.067x), where x = 7 corresponds to the year 2007. Find the assets in 2011 by substituting 11 for x and evaluate to find A(x).

Learn how to calculate the financial assets of a firm in 2011 using the exponential growth formula A(x) = 323e^(0.067x). This example covers key algebraic concepts and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation