We are just starting polynominals and this is a problem I am struggling with, its about Saving for College and here it is word for word:

SAVING FOR COLLEGE In this project, you will forecast a friend's finances. Jane has received $75 from her grandparents on every birthday since she was one year old. She has been saving the money in an account that pays 5% interest. She is saving her money to help you pay for her college education, which she will start this fall after her 18th birthday. She also has been receiving birthday checks from her other relatives, but these didn't start until she was 12 years old. The amounts of these checks from her 12th birthday until her 18th birthday are $45, $45, $55, $50, $55, $60, $65.

How much money will she have saved just from her birthdays by the time she starts college? IS this a reasonable amount to pay for a used car during her junior year in college? If she had invested her money in a different accoutn that had earned 7% interest, how much more money would she have saved?

Follow these steps to accomplish your task.

0. -Construct a pattern for this situation
1. -Develop a polynomial model to describe the amount she has each year
2. -Determine the amount of money she received on birthdays 12 through 18
3. -Determine what needs to be changed in your model when changing the interest rate.
4. -Write a paragraph describing the problem and your solution.

PLEASE, help me to learn how to complete all steps of this problem correctly. I am very eager to learn how to do this. Thanks you VERY much for your time and help.

Sincerely,

Andrew Kunz

I hope that I can get you started on this problem. You said that the interest rate is 5% so I am going to assume that this means %5 per year. What that means is that if I have say $90 in this account then, one year later the amount in the account will $90 plus 5% of $90, that is $(90+0.05x90)=$90(1.05)

Below I constructed a table to keep track of a few years.

1. On her 1st birthday Jane receives $75.

2. On her 2nd birthday she receives another $75 and in her account is the $75 she received the year before, which is now worth $75(1.05). Hence in total she has $75+$75(1.05).

3. On her 3rd birthday she receives a further $75 and in her account is the $75+$75(1.05) she had on her 2nd birthday, which is now worth ($75+$75(1.05))(1.05). Hence in total she has $75+$75(1.05)+$75(1.05)².

I hope this helps,
Penny