Question

the assets (in billions of dollars) for a financial firm can be approximated by the function ( a(x) = 333e^{.055x} ), where ( x = 7 ) corresponds to the year 2007. find the assets in each of the following years.
(a) 2012
(b) 2016
(c) 2019
(a) which of the following describes how to find the assets in 2012 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 2012, substitute ( \boldsymbol{12} ) for ( x ) and evaluate to find ( a(x) ).
b. to find the assets in 2012, find the intersection point of the graphs ( y = 333e^{.055x} ) and ( y = \boldsymbol{square} ). the assets in 2012 are represented by the ( y )-coordinate.
in 2012 the assets are about $\boldsymbol{square}$ billion.
(type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate x for 2012

Since $x=7$ corresponds to 2007, $x = 2012 - 2007 + 7 = 12$

Step2: Substitute x=12 into A(x)

$A(12) = 333e^{0.055 \times 12}$
First compute the exponent: $0.055 \times 12 = 0.66$
Then calculate $e^{0.66} \approx 1.9348$
Finally: $A(12) = 333 \times 1.9348 \approx 644.3$

Step3: Verify method for 2012

The correct method is substituting $x=12$ into $A(x)$.

Answer:

(a) A. To find the assets in 2012, substitute 12 for x and evaluate to find A(x).
In 2012 the assets are about $\boldsymbol{644.3}$ billion.