To compare the two investment options, we need to evaluate them at 10 years.
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First Investment Option (exponential model): The equation is given by \( y = 20,000 e^{0.12x} \). Let's calculate y when \( x = 10 \):
\[ y = 20,000 e^{0.12 \times 10} = 20,000 e^{1.2} \]
Using the approximate value \( e^{1.2} \approx 3.3201 \):
\[ y \approx 20,000 \times 3.3201 \approx 66,402.00 \]
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Second Investment Option (from the table): From the table, when \( x = 10 \), \( y \) is given as \( 81,548.45 \).
Now, let’s compare the two options after 10 years:
- First Option: Approximately $66,402.00
- Second Option: $81,548.45
Now we can analyze the differences:
\[ 81,548.45 - 66,402.00 \approx 15,146.45 \]
Thus, the second investment option gives about $15,146.45 more than the first after 10 years.
Now, regarding the initial investments:
- The first investment option starts at a \( y \)-intercept of $20,000.
- The second investment option starts at a \( y \)-intercept of $30,000.
If Norma wants to invest as little money as possible upfront, she should choose the option with the smaller initial investment, which is the first option with a \( y \)-intercept of $20,000.
Final Decision:
Norma should select the first investment option since it has a y-intercept of $20,000.00.