Question

Norma seeks 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=20,000e
0.12x
. The second investment option is modeled by a table (not provided here).
Compare the two function models. If Norma wants to invest as little money as possible upfront, which option should she choose?
A. Norma should select the first investment option since it has a y-intercept of 20,00. B. Norma should select the second investment option since it has a y-intercept of 30. Norma seeks 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=20,000e
0.12x
. The second investment option is modeled by a table (not provided here).
Compare the two function models. If Norma wants to invest as little money as possible upfront, which option should she choose?
A. Norma should select the first investment option since it has a y-intercept of 20,000
B. Norma should select the second investment option since it has a y-intercept of 30,000
C. Norma should select the second investment because it will giver her around 13,000 more than the first option after 10 years
D. Norma should select the second investment because it will giver her around 15,000 more than the first option after 10 years

Answers

GPT-4o mini
To compare the two investment options effectively, we need to analyze the first investment option using the given exponential model and consider the implications of the second option based on the available information (though we don't have the actual table data for the second option).

The first investment option is given by the equation:

\[ y = 20,000 e^{0.12x} \]

In this equation:
- \( y \) represents the value of the investment after \( x \) years.
- The initial investment (y-intercept, when \( x = 0 \)) is $20,000.

### Analysis of the First Investment

We'll calculate the future value of this investment after 10 years:

1. Set \( x = 10 \):
\[
y = 20,000 e^{0.12 \times 10} = 20,000 e^{1.2}
\]

2. Using the approximate value of \( e^{1.2} \approx 3.3201 \):
\[
y \approx 20,000 \times 3.3201 \approx 66,402
\]

### Comparison With the Second Investment Option

We don't have the specific values from the second investment option's table, but based on the provided multiple-choice options, we can analyze the given statements:

- **A** states that the first option should be selected since it has a y-intercept of $20,000. This is true but does not consider the growth potential after 10 years.
- **B** states that Norma should select the second investment which has a y-intercept of $30,000. This is likely untrue as it suggests a higher upfront cost.
- **C** and **D** provide potential future values comparisons after 10 years, where the second option is said to give around $13,000 or $15,000 more than the first option.

### Conclusion

- If the second option truly does yield a notably higher return after 10 years as suggested in options C and D, then despite the higher upfront cost, it may be the more advantageous investment in terms of growth.
- However, without the actual table values for the second investment, we cannot definitively calculate or compare the returns.

### Recommendation

Thus, without additional data from the second option but based on potential return and if C and D are accurate, it suggests that the second investment might ultimately provide a better long-term benefit. Therefore, based on the choices:

**C or D** would be the recommended selections based on potential future earnings assuming they accurately reflect the second investment's performance.

### Final Answer
Since both C and D suggest that the second investment is more profitable after 10 years, I recommend:

**C or D (depending on which projected future value is more accurate).**

Related Questions