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 ( 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 = square ). the assets in 2012 are represented by the ( y )-coordinate.
in 2012 the assets are about ( $ 644.3 ) billion. (type an integer or a decimal rounded to the nearest tenth as needed.)
(b) which of the following describes how to find the assets in 2016 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 2016, find the intersection point of the graphs ( y = 333e^{.055x} ) and ( y = square ). the assets in 2016 are represented by the ( y )-coordinate.
b. to find the assets in 2016, substitute ( square ) for ( x ) and evaluate to find ( a(x) ).

Explanation:

Step1: Calculate x for 2012

$x = 2012 - 2007 = 5$

Step2: Verify 2012 calculation method

Option A is incorrect (uses x=12). Option B: Substitute $x=5$ into $A(x)=333e^{0.055x}$, solve for intersection with $y=644.3$.

Step3: Calculate x for 2016

$x = 2016 - 2007 = 9$

Step4: 2016 calculation method & value

Option B: Substitute $x=9$ into $A(x)=333e^{0.055x}$.
$A(9)=333e^{0.055\times9}=333e^{0.495}\approx333\times1.6407\approx546.35$

Step5: Calculate x for 2019

$x = 2019 - 2007 = 12$

Step6: Compute 2019 assets value

$A(12)=333e^{0.055\times12}=333e^{0.66}\approx333\times1.9348\approx644.3$

Answer:

(a) B. To find the assets in 2012, find the intersection point of the graphs $y = 333e^{0.055x}$ and $y=644.3$. The assets in 2012 are represented by the y-coordinate.
(b) B. To find the assets in 2016, substitute $9$ for x and evaluate to find $A(x)$. The assets in 2016 are $\approx546.4$ billion dollars.
(c) The assets in 2019 are $\approx644.3$ billion dollars.