Use x=1+r

Question

, where r is the interest rate paid each year. Write a model polynomial, C(x)
, that represents the final amount of an 8-year investment if $500 was deposited at the beginning of the first year, $800 was deposited at the beginning of the fourth year, and an additional $370 was deposited at the beginning of the eighth year.(1 point)
Responses

C(x)=500x8+800x4+370x
upper C left parenthesis x right parenthesis equals 500 x superscript 8 baseline plus 800 x superscript 4 baseline plus 370 x

C(x)=500x8+800x4+370
upper C left parenthesis x right parenthesis equals 500 x superscript 8 baseline plus 800 x superscript 4 baseline plus 370

C(x)=500x8+800x5+370x
upper C left parenthesis x right parenthesis equals 500 x superscript 8 baseline plus 800 x superscript 5 baseline plus 370 x

C(x)=500x+800x5+370x8

Answer 1

To model the final amount \( C(x) \) for the investments made over 8 years with different deposits, you will need to consider how long each deposit will earn interest.

1. The first deposit of $500 is made at the beginning of the first year and earns interest for 8 years, giving \( 500x^8 \).
2. The second deposit of $800 is made at the beginning of the fourth year and earns interest for 5 years, giving \( 800x^5 \).
3. The third deposit of $370 is made at the beginning of the eighth year and earns interest for 1 year, giving \( 370x^1 \) (or just \( 370x \)).

Putting these together, the model polynomial will be:

\[ C(x) = 500x^8 + 800x^5 + 370x \]

Based on the responses you provided, the correct answer is:

\[ C(x) = 500x^8 + 800x^5 + 370x \]