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) C(x) = 5000x + 2000x ^ 3; C(x) = 5000x ^ 7 + 7000x ^ 4; C(x) = 5000x ^ 7 + 2000x ^ 3; C(x) = 5000x ^ 7 + 2000x ^ 5

Answer 1

To build the model polynomial \( C(x) \) that represents the final amount of the investment over 7 years, we need to account for the different deposits made at different times and the growth of those deposits based on the interest rate.

1. First Deposit: $5,000 is deposited at the beginning of the first year. Since this amount is invested for 7 years, its growth can be represented as:

   \[ 5000x^7 \]

   where \( x = 1 + r \) represents the growth factor for 7 years.

2. Second Deposit: $2,000 is deposited at the beginning of the third year, which means it is invested for 5 years. Its growth can be represented as:

   \[ 2000x^5 \]

   where \( x = 1 + r \) accounts for the growth over those 5 years.

Combining both contributions, the total amount \( C(x) \) is given by:

\[ C(x) = 5000x^7 + 2000x^5 \]

Thus, the correct model polynomial representing the final amount of the investment after 7 years is:

\[ \boxed{C(x) = 5000x^7 + 2000x^5} \]