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)ResponsesC(x)=500x8+800x4+370xupper C left parenthesis x right parenthesis equals 500 x superscript 8 baseline plus 800 x superscript 4 baseline plus 370 xC(x)=500x+800x5+370x8upper C left parenthesis x right parenthesis equals 500 x plus 800 x superscript 5 baseline plus 370 x superscript 8 baselineC(x)=500x8+800x4+370upper C left parenthesis x right parenthesis equals 500 x superscript 8 baseline plus 800 x superscript 4 baseline plus 370C(x)=500x8+800x5+370x

Answer 1

To model the final amount of the investment over 8 years with different deposits made at different times, we need to consider how each deposit would grow with interest over the years.

1. The initial deposit of $500 at the beginning of the first year accumulates interest for 8 years:
   This is represented as \( 500x^8 \).

2. The deposit of $800 at the beginning of the fourth year accumulates interest for 5 years:
   This is represented as \( 800x^5 \).

3. The deposit of $370 at the beginning of the eighth year accumulates interest for 1 year:
   This is represented as \( 370x^1 \) or just \( 370x \).

Combining these, the model polynomial \( C(x) \) representing the final amount of the investment is:

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

So, the correct response is:

C(x) = 500x^8 + 800x^5 + 370x.