user $x = 1 + r$, where $r$ is the interest rate paid each year. write a model polynomial, $c(x)$ represent…

user $x = 1 + r$, 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 $2,000 was deposited at the beginning of the third year. (1 point)\n$c(x)=5,000x^{7}+7,000x^{4}$\n$c(x)=5,000x + 2,000x^{3}$\n$c(x)=5,000x^{7}+2,000x^{5}$\n$c(x)=5,000x^{7}+2,000x^{3}$

user $x = 1 + r$, 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 $2,000 was deposited at the beginning of the third year. (1 point)\n$c(x)=5,000x^{7}+7,000x^{4}$\n$c(x)=5,000x + 2,000x^{3}$\n$c(x)=5,000x^{7}+2,000x^{5}$\n$c(x)=5,000x^{7}+2,000x^{3}$

Answer

Explanation:

Step1: Analyze first - deposit

The $5000$ deposited at the beginning of the first year earns interest for 7 years. Using the compound - interest formula $A = P(1 + r)^n$, with $x=1 + r$, the amount it grows to is $5000x^{7}$.

Step2: Analyze second - deposit

The $2000$ deposited at the beginning of the third year earns interest for $7 - 2=5$ years. Using the compound - interest formula $A = P(1 + r)^n$, with $x = 1 + r$, the amount it grows to is $2000x^{5}$.

Step3: Combine amounts

The final amount polynomial $C(x)$ is the sum of the amounts from the two deposits, so $C(x)=5000x^{7}+2000x^{5}$.

Answer:

C. $C(x)=5000x^{7}+2000x^{5}$