Use x=1+r , where r is the interest rate paid each year. Write a model polynomial, C(x) . Represent the final amount of a 7-year investment if $5,000 was deposited at the beginning of the first year, and $2,000 was deposited at the beginning of the third year.(1 point)

Question

Use x=1+r , where r is the interest rate paid each year. Write a model polynomial, C(x) . Represent the final amount of a 7-year investment if $5,000 was deposited at the beginning of the first year, and $2,000 was deposited at the beginning of the third year.(1 point)

1. C(x) = 5,000x^7 + 2,000x^3
2. C(x) = 5,000x + 2,000x^3
3. C(x) = 5,000x^7 + 7,000x^4
4. C(x) = 5,000x^7 + 2,000x^4

Answer 1

The correct answer is option 4.

The 7-year investment can be broken down into two parts:

1. The $5,000 deposit at the beginning of the first year, which will grow for 7 years with interest. This can be represented as: $5,000x^7.
2. The $2,000 deposit at the beginning of the third year, which will grow for 5 years with interest (since it was deposited 2 years later). This can be represented as: $2,000x^4.

Adding both parts together gives us the model polynomial: C(x) = 5,000x^7 + 2,000x^4.

Answer 2

The correct answer is 4. C(x) = 5,000x^7 + 2,000x^4.

To calculate the final amount of a 7-year investment, we need to determine how each deposit grows over time. The equation x = 1 + r represents the growth factor for each year, where r is the interest rate paid each year.

Since $5,000 was deposited at the beginning of the first year, it will grow for all 7 years. So, we multiply this deposit by x^7.

Since $2,000 was deposited at the beginning of the third year, it will only grow for 5 years (from the third year to the seventh year). So, we multiply this deposit by x^4.

Therefore, the model polynomial C(x) represents the final amount of the investment as the sum of the growth of both deposits: C(x) = 5,000x^7 + 2,000x^4.

Answer 3

To solve this problem, we need to use the given formula for the model polynomial and plug in the values for the deposits at each year.

According to the problem, $5,000 was deposited at the beginning of the first year, which corresponds to x^1 in the formula. And $2,000 was deposited at the beginning of the third year, which corresponds to x^3 in the formula.

Therefore, the correct model polynomial C(x) would include these terms.

Option 1: C(x) = 5,000x^7 + 2,000x^3

This option correctly includes the terms representing the deposits made in the first and third years, as required by the problem. Thus, the correct answer is 1. C(x) = 5,000x^7 + 2,000x^3.