Use x=2+r, where r is the interest rate paid each year. Write a model polynomial c(x) that represents the final amount of an 7-year investment if $400 was deposited at the beginning of t e first year, $900 was deposited at the beginning of the fourth year, and an additional $350 was deposited at the beginning of the eighth year.

Question

1)C(x)=400x^8 +900x^4 +350x
2)C(x)=400x^8 +900x^5 +350x
3)C(x)=400x^8 +900x^4 +350
4)C(x)=400x+900x^5 +370x^8

Answer 1

To model the final amount of a 7-year investment using the given parameters, we need to determine the contribution of each deposit over time and how they accrue interest.

1. Initial Deposit ($400):

   • This amount is deposited at the beginning of the first year and earns interest for 7 years:
   • Contribution = \( 400 \cdot x^7 \)

2. Second Deposit ($900):

   • This amount is deposited at the beginning of the fourth year and earns interest for 4 years:
   • Contribution = \( 900 \cdot x^4 \)

3. Third Deposit ($350):

   • This amount is deposited at the beginning of the eighth year and earns interest for 0 years (it will not earn any interest in this 7-year span):
   • Contribution = $350 (the amount remains unchanged as it does not earn interest)

So, the total amount after 7 years, \( C(x) \), can be expressed as:

\[ C(x) = 400x^7 + 900x^4 + 350 \]

Now let's look at the provided options:

1. \( C(x) = 400x^8 + 900x^4 + 350x \)
2. \( C(x) = 400x^8 + 900x^5 + 350x \)
3. \( C(x) = 400x^8 + 900x^4 + 350 \)
4. \( C(x) = 400x + 900x^5 + 370x^8 \)

None of these options match the correct expression \( C(x) = 400x^7 + 900x^4 + 350 \).

Therefore, it looks like there may be an error in the formulation or options provided, as the correct polynomial for your scenario is not listed. However, the closest one in terms of terms would be option 3, except it incorrectly has \( 400x^8 \) instead of \( 400x^7 \).