The ordered pairs model an exponential decay function. {(−1,30), (0,21), (1,14.7), (2,10.2 9)} what is the function equation? enter your answer in the box. f(x)=

The function equation is;

Step-by-step explanation:

An exponential decay function is in the form of   ......[1]

where a≠0 is the initial value and b≠0, .

Consider any two ordered pairs to modeled the function:

(-1 , 30) and (0, 21)

Substitute these value to get a and b value ;

For (0, 21)

put x = 0 and y = 21 in [1] we get

or

21 = a

Similarly,

substitute (-1 , 30) we get;

or

Substitute the value of a to solve for b;

Divide both sides by 30 we get;

or

b = 0.7 < 1

Value of a = 21 and b= 0.7

Substitute these values in [1] to get the required function:

therefore, the function equation is;

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

answer: 2530

hope this