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)

Question

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