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.
To model the final amount of a 7-year investment using the given information, we can break it down into three parts:
1. The initial deposit of $5,000 at the beginning of the first year will earn interest for 7 years.
2. The deposit of $2,000 at the beginning of the third year will earn interest for 5 years.
3. The interest earned from both deposits will accumulate over the 7-year period.
Let's calculate each part separately:
1. The initial deposit of $5,000:
Since this deposit earns interest for all 7 years, we can use the formula C(x) = P(x)^n, where P(x) represents the principal amount and n is the number of years. In our case, P(x) = $5,000 and n = 7. Applying the formula, we get:
C(x) = (1+r)^7 * $5,000
2. The deposit of $2,000 at the beginning of the third year:
Since this deposit only earns interest for the last 5 years, we need to multiply it by (1+r)^5. So, this part can be represented as:
C(x) = $2,000 * (1+r)^5
3. Accumulated interest from both deposits:
Since we want to find the final amount, we need to add the amounts from both deposits, which gives us:
C(x) = (1+r)^7 * $5,000 + $2,000 * (1+r)^5
Therefore, the model polynomial for the final amount of the 7-year investment would be:
C(x) = (1+r)^7 * $5,000 + $2,000 * (1+r)^5
To calculate the final amount for the investment, we can use the given equation x = 1 + r, where r is the interest rate paid each year. We need to create a model polynomial, C(x), to represent the final amount.
Step 1: Determine the number of terms in the polynomial:
Since the investment is made for 7 years and two deposits are made at the beginning of different years, we will have 7 terms in the polynomial.
Step 2: Identify the coefficients and exponents for each term:
The first deposit made at the beginning of the first year is $5,000, which will have an exponent of 1 since it is deposited in the first year.
The second deposit made at the beginning of the third year is $2,000, so it will have an exponent of 3 since it is deposited in the third year.
Step 3: Write the model polynomial, C(x):
C(x) = 5000*x^1 + 2000*x^3
This polynomial represents the final amount of the 7-year investment with $5,000 deposited at the beginning of the first year and $2,000 deposited at the beginning of the third year.