Question

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

Answer 1

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 

Answer 2

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