1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nina [5.8K]
3 years ago
15

I really need help with this, lol: Using the table of values given, determine the equation of the function that would model this

data:

Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0
Somewhat optimistically, we guess that this function is a polynomial, since it doesn't immediately look like it follows an exponential or logarithmic pattern.

We can solve for the equation of degree n passing through n points by writing the polynomial in the form:

c_n x^n + c_{n-1} x^{n-1} + \cdots + c_0 = f(x).

Then, we solve for the values of the sequence c by substituting in n pairs (x, f(x)).  This gives us the polynomial of degree n satisfying the conditions for the first n points; afterwards, we have to check if this polynomial works for the other points.  If it does, it is the solution, otherwise, we need to keep going.

Testing in this manner, degrees zero, one, and two don't work.  When we try degree three, however, we get the system of equations:

c_3+c_2+c_1+c_0=0
8c_3+4c_2+2c_1+c_0=3
27c_3+9c_2+3c_1+c_0=16
64c_3+16c_2+4c_1+c_0=45

Solving this system gives c_3 = 1, c_2 = -1, c_1 = -1, c_0 = 1.  Substituting 5 into this polynomial, 5^3-5^2-5+1=96.  Likewise, f(6) = 175, so this polynomial satisfies all of the conditions listed.

We therefore conclude that f(x) = \boxed{x^3-x^2-x+1}.
You might be interested in
Marie has one 6-sided cube with the last 6 letters of the alphabet. She has another 6-sided cube with the first 6 letters of the
stiv31 [10]
I think it’s B because you have to find probability

But I’m not sure
7 0
3 years ago
Five wholes - four fifth
Tpy6a [65]

Answer: 4 and 1/5

Step-by-step explanation:

4 and 1/5

3 0
3 years ago
What is $250.14 -25.14
meriva

225


Step-by-step explanation:

Look it up on google.

7 0
3 years ago
Read 2 more answers
A "point" is 1% of your borrowed amount on a mortgage. You want to pay 2 points to get a 0.5% reduction in your interest rate on
zzz [600]
Hi there:)

One point is 1%
Two points 2%

You want to pay two points so
175,000×0.02=3,500 ....answer

Hope it helps
5 0
3 years ago
HELP PLEASE! 40 POINTS AND WILL MARK BRAINLIEST.
pshichka [43]

Answer:

Explicit rule, because you can find the 40th term directly using the explicit rule. You would need to find the first 39 terms before finding the 40th terms using recursive rule.

hope this helps...

3 0
3 years ago
Other questions:
  • Explain how to use hundredths grids to subtract 1.65 - 0.98
    6·1 answer
  • √x • 4√x how do I simplify this?
    14·2 answers
  • A weather balloon holds 2,850 cubic meters of helium. The density of helium is 0.1685 kilograms per cubic meter. How many kilogr
    12·2 answers
  • The graph of | x | is the solid black graph below. Which function represents the dotted graph? (pls help)
    8·1 answer
  • Does the graph represent an arithmetic sequence or geometric sequence?
    10·1 answer
  • Solve the system of equations x+y=-1 and 5x-7y=79 by combining the equations.
    15·1 answer
  • The product of -3x and (2x+5) is …​
    9·2 answers
  • If X=sin 130° + cos 130° then<br>1)X&lt;0 2)X=0 3)X&gt;0 4)X greater than or equal to 0​
    7·1 answer
  • HELP PLSSS Function g is a transformation x of f(x) = 2 ^ x Select all the true statements about the functions. (F-|F.2.4)
    12·1 answer
  • Everyone if you can help that would be great
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!