Question

User x=1+r, where r is the interest rate paid each year. Write a model polynomial, C(x). Represent the final amount of a 7-year investment if $5,000 was deposited at the beginning of the first year, and $2,000 was deposited at the beginning of the third year. (1 point)
Responses

C(x)=5,000x7+2,000x5
cap c times x is equal to 5 comma 000 x to the 7th power plus 2 comma 000 x to the 5th power

C(x)=5,000x7+7,000x4
cap c times x is equal to 5 comma 000 x to the 7th power plus 7 comma 000 x to the 4th power

C(x)=5,000x7+2,000x3
cap c times x is equal to 5 comma 000 x to the 7th power plus 2 comma 000 x cubed

C(x)=5,000x+2,000x3

Answer 1

To model the final amount of a 7-year investment where $5,000 is deposited at the beginning of the first year and $2,000 is deposited at the beginning of the third year, we can use the formula based on compound interest.

### Breakdown of Contributions:

1. **First Deposit ($5,000)**:
- This amount is deposited at the beginning of the first year and will earn interest for 7 years.
- The future value of this investment is represented by \( 5,000 \cdot x^7 \) (where \( x = 1 + r \)).

2. **Second Deposit ($2,000)**:
- This amount is deposited at the beginning of the third year and will earn interest for 5 years.
- The future value of this investment is represented by \( 2,000 \cdot x^5 \).

### Final Model:
Therefore, the total future value after 7 years, \( C(x) \), can be modeled as:
\[
C(x) = 5,000x^7 + 2,000x^5
\]

### Correct Response:
The correct polynomial model is:
**C(x) = 5,000x^7 + 2,000x^5**