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polet [3.4K]
3 years ago
8

Give a possible formula for the function below. Let A = (-1, 32) and B = (1, 8). (Note: Use the general exponential function.)

Mathematics
2 answers:
skelet666 [1.2K]3 years ago
8 0
The question ask to find and compute the possible formula for the function below where as A = (-1,32) and B= (1,8).  In my own calculation and further computation about the problem and also following the rule of general exponential function, the formula would be y = a*(b^x). I hope this would help 
Svetach [21]3 years ago
3 0

Step-by-step explanation:

Let the equation is y = ab^x  ............ (1)

Putting the values of point A in equation (1) as follows.

                  y = ab^x

                  32 = ab^(-1) ........... (2)

Putting the values of point B in equation (1) as follows.

                  y = ab^x

                  8 = ab^(1) ................ (3)

Now, divide the equation (2) by equation (3) as follows.

            \frac{32}{8} = \frac{ab^(-1)}{ab^(1)}

Cancelling out with common factors, the equation will be written as follows.

             4 = \frac{b^{-1}}{b^1}

             4 = \frac{1}{b^1 \times b^{1}}

             4 = \frac{1}{b^2}

or,          b^{2} = \frac{1}{4}

Taking square root on both the side, we get

               b = ± \frac{1}{2}

Case 1. Place the value of b = +\frac{1}{2} in equation (3) as follows.

            8 = ab^1

            8 = a(\frac{1}{2})^{1}

            8 \times 2 = a

                      a = 16

Case 2. Place the value of b = -\frac{1}{2} in equation (3) as follows.

             8 = ab^1

                  8 = a \times (\frac{-1}{2})^{1}

            - 8 \times 2 = a

                      a = - 16

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