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)

Responses

C(x)=5,000x7+2,000x3
upper C left parenthesis x right parenthesis equals 5,000 x superscript 7 baseline plus 2,000 x cubed

C(x)=5,000x7+7,000x4
upper C left parenthesis x right parenthesis equals 5,000 x superscript 7 baseline plus 7,000 x superscript 4 baseline

C(x)=5,000x7+2,000x4
upper C left parenthesis x right parenthesis equals 5,000 x superscript 7 baseline plus 2,000 x superscript 4 baseline

C(x)=5,000x+2,000x3

3 answers

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

To write a model polynomial, C(x), representing the final amount of a 7-year investment, we need to consider the deposits made at the beginning of each year.

In this case, $5,000 was deposited at the beginning of the first year, and $2,000 was deposited at the beginning of the third year.

To calculate the final amount, we need to consider the effect of the interest rate, r, on these deposits. Given that x = 1 + r, we can use the following equation:

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

Here, x^7 represents the effect of the interest rate on the $5,000 deposit over 7 years, and x^4 represents the effect of the interest rate on the $2,000 deposit over 4 years. Therefore, this equation accurately models the final amount of the 7-year investment.