Use the table to answer the 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 $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 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 first investment option since it has a y-intercept of $20,000.00. Norma should select the first investment option since it has a y -intercept of $20,000.00. 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 has a y -intercept of $30,000.00. Skip to navigation

1 answer

To compare the two investment options, we need to evaluate the amounts in both options after 10 years.

  1. Investment Option 1 (Exponential Growth Model): This option is modeled by the equation: \[ y = 20,000e^{0.12x} \] Substituting \( x = 10 \): \[ y = 20,000e^{0.12 \times 10} = 20,000e^{1.2} \] Calculating \( e^{1.2} \) (approximately 3.3201): \[ y = 20,000 \times 3.3201 \approx 66,402.06 \]

  2. Investment Option 2 (Table Values): From the table, the amount after 10 years is: \[ y = 81,548.45 \]

Now we can compare the two amounts after 10 years:

  • Option 1: $66,402.06
  • Option 2: $81,548.45

Now we calculate the difference between the two options after 10 years: \[ 81,548.45 - 66,402.06 = 15,146.39 \]

Based on the comparison:

  • The second investment option (the table) gives around $15,000 more than the first option after 10 years.

Lastly, let's consider the initial investments:

  • Investment Option 1 has an initial investment of $20,000.
  • Investment Option 2 has an initial investment of $30,000.

Since Norma wants to invest as little money as possible up front, she would choose Investment Option 1, even though the second option yields more after 10 years, it requires a higher initial investment.

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