Question

the assets (in billions of dollars) for a financial firm can be approximated by the function ( a(x) = 333e^{0.055x} ), 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 (square) for ( x ) and evaluate to find ( a(x) ).
b. to find the assets in 2012, find the intersection point of the graphs ( y = 333e^{0.055x} ) and ( y = square ). the assets in 2012 are represented by the ( y )-coordinate.

Explanation:

Step1: Calculate x for 2012

$x = 2012 - 2007 = 5$

Step2: Calculate x for 2016

$x = 2016 - 2007 = 9$

Step3: Calculate x for 2019

$x = 2019 - 2007 = 12$

Step4: Evaluate A(5) for 2012

$A(5) = 333e^{0.055 \times 5} = 333e^{0.275} \approx 333 \times 1.3165 = 438.4$

Step5: Evaluate A(9) for 2016

$A(9) = 333e^{0.055 \times 9} = 333e^{0.495} \approx 333 \times 1.6405 = 546.3$

Step6: Evaluate A(12) for 2019

$A(12) = 333e^{0.055 \times 12} = 333e^{0.66} \approx 333 \times 1.9348 = 644.3$

Step7: Choose correct 2012 method

Option A: Substitute $x=5$ into $A(x)$.

Answer:

Part (a)

• Correct choice: A. To find the assets in 2012, substitute $\boldsymbol{5}$ for x and evaluate to find A(x).
• Assets in 2012: $\boldsymbol{438.4}$ billion dollars

Part (b)

Assets in 2016: $\boldsymbol{546.3}$ billion dollars

Part (c)

Assets in 2019: $\boldsymbol{644.3}$ billion dollars