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)
1. C(x)=500x+800x^5+370x^8
2. C(x)=500x^8+800x^5+370x
3. C(x)=500x+800x^4+370x^8
4. C(x)=500x+800x^4+370
The correct answer is:
3. C(x) = 500x + 800x^4 + 370x^8
The correct answer is option 3.
The polynomial should include the deposits made at the beginning of the first, fourth, and eighth years, which are represented by the terms $500x$, $800x^4$, and $370x^8$ respectively. Therefore, the model polynomial that represents the final amount of the investment is:
C(x) = 500x + 800x^4 + 370x^8
To write a model polynomial, C(x), that represents the final amount of the investment, we need to consider the deposits made at different times and the interest earned each year.
First, let's break down the problem statement:
- $500 was deposited at the beginning of the first year.
- $800 was deposited at the beginning of the fourth year.
- An additional $370 was deposited at the beginning of the eighth year.
We know that the initial amount invested is $500, which can be represented as 500x^0.
For the $800 deposit in the fourth year, we need to account for the interest earned from the first to the fourth year. The interest earned accumulates over the years and can be represented as 800x^4.
Finally, for the additional $370 deposit in the eighth year, we need to consider the interest earned from the first to the eighth year. This can be represented as 370x^8.
Now, let's add up all these components to form the model polynomial, C(x):
C(x) = 500x^0 + 800x^4 + 370x^8
Therefore, the correct answer is option 3: C(x) = 500x + 800x^4 + 370x^8.