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.
C(x) = 500x + 800x^5 + 370x^8
C(x) = 500x^8 + 800x^4 + 370x
C(x) = 500x^8 + 800x^4 + 370
C(x) = 500x^8 + 800x^5 + 370x
C(x) = 500x + 800x^4 + 370x^7
The correct model polynomial, C(x), that represents the final amount of an 8-year investment is:
C(x) = 500x + 800x^4 + 370x^7
To construct the model polynomial C(x), we need to consider the timeline of the investment and the corresponding amounts deposited at the beginning of each year.
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.
Let's break down the calculation step by step:
1. At the beginning of the first year, $500 was deposited. This amount is represented by the term 500x since x = 1 + r.
2. At the beginning of the fourth year, $800 was deposited. Since x = 1 + r, the term representing this deposit will be 800x^4, as it signifies the growth of the deposit over the following 4 years.
3. At the beginning of the eighth year, an additional $370 was deposited. Again, using x = 1 + r, the term representing this deposit will be 370x^8, as it signifies the growth of the deposit over the following 8 years.
Combining all three deposits, we obtain the model polynomial:
C(x) = 500x + 800x^4 + 370x^8
Therefore, the correct model polynomial representing the final amount of the 8-year investment is C(x) = 500x + 800x^4 + 370x^8.