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
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
Answers
GPT 3.5
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.
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.