Question

Use x=1+r
, 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)=500x+800x5+370x8
upper C left parenthesis x right parenthesis equals 500 x plus 800 x superscript 5 baseline plus 370 x superscript 8 baseline

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+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+800x5+370x

Answer 1

To model the final amount \( C(x) \) after an 8-year investment with given deposits at specified times, we need to account for how long each deposit will earn interest by the end of the 8 years.

1. The $500 deposit at the beginning of the first year will be invested for 8 years. Thus, this amount will be represented as:
\[
500x^8
\]

2. The $800 deposit at the beginning of the fourth year will be invested for 5 years (from year 4 to year 8). Thus, this amount will be represented as:
\[
800x^5
\]

3. The $370 deposit at the beginning of the eighth year will not earn any interest since it is deposited at the beginning of year 8. Thus, this amount is simply:
\[
370
\]

Putting it all together, the model polynomial \( C(x) \) is given by:
\[
C(x) = 500x^8 + 800x^5 + 370
\]

Therefore, the correct response is:
\[
C(x) = 500x^8 + 800x^5 + 370
\]