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)=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)=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+800x5+370x
C(x)=500x^8+800x^4+370x
The correct answer is:
C(x) = 500x^8 + 800x^4 + 370x
To write the model polynomial, C(x), that represents the final amount of the investment, we need to understand the given information.
From the given information, we know that $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.
The polynomial representation will consist of terms that represent the amount deposited at each year multiplied by the corresponding power of x.
Let's break it down step by step:
1. For the $500 deposited at the beginning of the first year, we multiply it by x raised to the power of 8 since it will accumulate for 8 years.
2. For the $800 deposited at the beginning of the fourth year, we multiply it by x raised to the power of 4 since it will accumulate for 4 years.
3. For the additional $370 deposited at the beginning of the eighth year, we just include it as a constant term since it will not accumulate any further.
Putting it all together, the correct model polynomial is:
C(x) = 500x^8 + 800x^4 + 370
Therefore, the option is:
C(x) = 500x^8 + 800x^4 + 370x