To compare the two investment options, we need to evaluate the amounts in both options after 10 years.
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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): \[ y = 20,000 \times 3.3201 \approx 66,402.06 \]
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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.