To compare the two investment options, we will first evaluate the first investment option using the provided exponential model \( y = 20,000e^{0.12x} \) at \( x = 10 \) years:
- Calculate the first investment option after 10 years: \[ y = 20,000e^{0.12 \cdot 10} \] \[ y = 20,000e^{1.2} \] Using \( e^{1.2} \approx 3.32011692 \): \[ y \approx 20,000 \cdot 3.32011692 \approx 66,402.34 \]
So, the first investment option will yield approximately \( $66,402.34 \) after 10 years.
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From the table, we know that the second investment option at \( x = 10 \) years has \( y \approx 81,548.45 \) (given directly in the table).
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Comparison after 10 years:
- First option: \( \approx 66,402.34 \)
- Second option: \( 81,548.45 \)
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Difference: \[ 81,548.45 - 66,402.34 \approx 15,146.11 \]
So, the second investment option gives approximately \( $15,000.00 \) more than the first option after 10 years.
Conclusion:
Given that the second investment option, which requires an initial investment of $30,000.00, yields more money than the first option after 10 years, while the first option has an initial investment of only $20,000, we can conclude:
Norma should select the second investment option since it will give her around $15,000.00 more than the first option after 10 years.
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