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)ResponsesC(x)=5,000x7+2,000x5cap c times x is equal to 5 comma 000 x to the 7th power plus 2 comma 000 x to the 5th powerC(x)=5,000x+2,000x3cap c times x is equal to 5 comma 000 x plus 2 comma 000 x cubedC(x)=5,000x7+2,000x3cap c times x is equal to 5 comma 000 x to the 7th power plus 2 comma 000 x cubedC(x)=5,000x7+7,000x4cap c times x is equal to 5 comma 000 x to the 7th power plus 7 comma 000 x to the 4th power

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 create a polynomial \( C(x) \) to represent the total amount after 7 years.

1. The first deposit of $5,000 grows for 7 years. Its contribution to the total amount can be represented as:
\[
5,000x^7
\]
where \( x = 1 + r \).

2. The second deposit of $2,000 grows for 5 years (since it is made at the beginning of the third year). Its contribution can be represented as:
\[
2,000x^5
\]

Putting both contributions together, the model polynomial \( C(x) \) is:
\[
C(x) = 5,000x^7 + 2,000x^5
\]

Thus, the correct option from the responses provided is:
**C(x) = 5,000x^7 + 2,000x^5**.