SOLUTION: how much something is going to be used for a variable number of days. IN 1, 2, 3, 4, 5, 6, 7, 8 OUT 2, 5, 9, 14, 20, 27, 35, 44

Question 252448: how much something is going to be used for a variable number of days.
IN 1, 2, 3, 4, 5, 6, 7, 8
OUT 2, 5, 9, 14, 20, 27, 35, 44
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
I think you are trying to create a formula for this set of data. There are two ways - (1) use a graphing utility and the list functions, (2) paper and pencil.
I will go through the paper pencil approach.
step 1: list the outputs: 2, 5, 9, 14, 20, 27, 35, 44.
step 2: take successive differences: 5-2 = 3, 9-5 = 4, 14-9 = 5, 20-14 = 6, 27-20 = 7, and so on. Notice this "first level" of successive differences is 3, 4, 5, 6, 7, 8, 9. They are all not the same.
step 3: take a "second level" of successive differences: we get 1, 1, 1, 1, 1, and so on. We have the first part of our equation at 1x^2 / 2!. The general rule for this is
[successive difference number] X ^(number of levels it took) / (number of levels!)
step 4: put in the numbers 1, 2, and 3 for x to get: 1/2, 4/2, 9/2.
step 5: subtract these from our first three outputs to get:
2-1/2 = 3/2, 5-4/2 = 6/2, 9-9/2 = 9/2
step 6: With the answers from step 5, take successive differences. we get 3/2, 3/2, 3/2. We have the second part of our equation at (3/2)X^1 / 1!.
Step 7: putting the information from step 3 and step 6 together, we get
x^2/2 + 3x/2. This is the equations that models your data set.

RELATED QUESTIONS
A cute otisis media, an infection of the middele ear, is a common childhood illness.... (answered by haileytucki,Alan3354)

1. A rectangular room has a length of 12 feet, a width of 14 feet, and a height of 8... (answered by Fombitz)

1. Which of the following values is NOT equal to 34(58+9)? A. 34 x 67 B. 58(34+9) C.... (answered by Fombitz)

Refer to the North Valley Real Estate data, which report information on homes sold during (answered by Alan3354,ikleyn)

I have exam tomorrow. Please help me tutors. 1)AOB is a straight line. Find z if x=35... (answered by fcabanski)

A pharmacist working in Black lion Specialized Hospital wants to secure the availability... (answered by ikleyn)

What are the answers to all of these questions? 1. -6k+7k 2. 12r-8-12 3.... (answered by Fombitz)

Please help me solve these problems: "Find the rule to fit this In/Out tables. You may (answered by josgarithmetic)

A pharmacist working in Black lion Specialized Hospital wants to secure the availability... (answered by ikleyn)