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
