Question
Use x = 1 + r, where r is the interest rate paid each year. Write a polynomial model, 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
cap c times x is equal to 500 x to the 8th power plus 800 x to the 4th power plus 370 x
C(x)=500x+800x5+370x8
cap c times x is equal to 500 x plus 800 x to the 5th power plus 370 x to the 8th power
C(x)=500x8+800x4+370x
cap c times x is equal to 500 x to the 8th power plus 800 x to the 4th power plus 370 x
C(x)=500x8+800x5+370x
Responses
C(x)=500x8+800x4+370x
cap c times x is equal to 500 x to the 8th power plus 800 x to the 4th power plus 370 x
C(x)=500x+800x5+370x8
cap c times x is equal to 500 x plus 800 x to the 5th power plus 370 x to the 8th power
C(x)=500x8+800x4+370x
cap c times x is equal to 500 x to the 8th power plus 800 x to the 4th power plus 370 x
C(x)=500x8+800x5+370x
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To create a polynomial model \( C(x) \) that represents the final amount of an 8-year investment with the specified deposits, we need to analyze each deposit and how long it will earn interest.
1. The first deposit of $500 is made at the beginning of the first year. This amount will earn interest for 8 years. Thus, the contribution from this deposit is \( 500x^8 \).
2. The second deposit of $800 is made at the beginning of the fourth year. This amount will earn interest for 5 years (from the start of year 4 to year 8). Thus, the contribution from this deposit is \( 800x^5 \).
3. The third deposit of $370 is made at the beginning of the eighth year. This amount will earn interest for 1 year. Thus, the contribution from this deposit is \( 370x \).
Putting all of these together, the polynomial model for the final amount \( C(x) \) after 8 years is:
\[
C(x) = 500x^8 + 800x^5 + 370x
\]
So the correct response is:
**C(x) = 500x^8 + 800x^5 + 370x**.
1. The first deposit of $500 is made at the beginning of the first year. This amount will earn interest for 8 years. Thus, the contribution from this deposit is \( 500x^8 \).
2. The second deposit of $800 is made at the beginning of the fourth year. This amount will earn interest for 5 years (from the start of year 4 to year 8). Thus, the contribution from this deposit is \( 800x^5 \).
3. The third deposit of $370 is made at the beginning of the eighth year. This amount will earn interest for 1 year. Thus, the contribution from this deposit is \( 370x \).
Putting all of these together, the polynomial model for the final amount \( C(x) \) after 8 years is:
\[
C(x) = 500x^8 + 800x^5 + 370x
\]
So the correct response is:
**C(x) = 500x^8 + 800x^5 + 370x**.
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