Use the table to answer the question.

Question

Years, x 0 5 10 15
Money in Account, y (in $) 30,000.00 49,461.64 81,548.45 134,450.67
Norma seeks out the help of a financial advisor to discuss plans that will help her earn money over time on an initial investment. The advisor offers her two plans that will allow her to retire at the age of 50. The first investment option can be modeled by the equation y=20,000e0.12x
, while the second investment option is modeled by the table. Compare the two function models. If Norma wants to invest as little money as possible up front, which option should she choose?

(1 point)
Responses

Norma should select the second investment option since it will give her around $13,000.00 more than the first option after 10 years.
Norma should select the second investment option since it will give her around $13,000.00 more than the first option after 10 years.

Norma should select the second investment option since it has a y-intercept of $30,000.00.
Norma should select the second investment option since it has a y -intercept of $30,000.00.

Norma should select the second investment option since it will give her around $15,000.00 more than the first option after 10 years.
Norma should select the second investment option since it will give her around $15,000.00 more than the first option after 10 years.

Norma should select the first investment option since it has a y-intercept of $20,000.00.

Answer 1

To determine which investment option Norma should choose, we need to analyze the financial growth of both options after 10 years.

1. First Investment Option:

   • The equation is given by \( y = 20,000 e^{0.12x} \).
   • After 10 years (when \( x = 10 \)): \[ y = 20,000 e^{0.12 \times 10} = 20,000 e^{1.2} \approx 20,000 \times 3.3201 \approx 66,402.00. \]

2. Second Investment Option:

   • From the table, the value of money in the account after 10 years is \( y = 81,548.45 \).

Now, let's analyze the outcomes:

• The first investment option will be worth approximately $66,402.00 after 10 years.
• The second investment option will be worth $81,548.45 after 10 years.

To compare the two options after 10 years:

• The second investment option gives about \( 81,548.45 - 66,402.00 = 15,146.45 \), which we can round to approximately $15,000.00 more than the first option after 10 years.

Select the Best Option

The options provided indicate that if Norma wants to invest as little money as possible up front, she should select the second investment option since it provides a greater return compared to the first option.

Correct Response: Norma should select the second investment option since it will give her around $15,000.00 more than the first option after 10 years.