User x=1+r

Question

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

C(x)=5,000x7+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)=5,000x+2,000x3

Answer 1

In this investment scenario, we need to account for the compounded interest for each deposit separately.

1. The first deposit of $5,000 is made at the beginning of the first year and will be invested for 7 years. The final amount for this deposit can be represented as \(5,000x^7\), where \(x = 1 + r\).

2. The second deposit of $2,000 is made at the beginning of the third year, which means it will be invested for 5 years (from the end of year 2 to the end of year 7). The final amount for this deposit can be represented as \(2,000x^5\).

Therefore, the correct polynomial modeling the final amount of the investments in terms of \(x\) is:

\[ C(x) = 5,000x^7 + 2,000x^5 \]

The appropriate response is:

C(x) = 5,000x^7 + 2,000x^5.