Answer:
The exponential function is \(y=\frac{9}{2}(\frac{1}{2})^x\).
Step-by-step explanation:
We are given,
The function \(y=ab^x\) that passes through the points (-4,72) and (-2,18).
Substituting the values of x and y in the equation gives us,
\(72=ab^{-4}\) ................(1)
\(18=ab^{-2}\) ..................(2)
Dividing equation (1) by (2), we get,
\(\frac{72}{18}=\frac{ab^{-4}}{ab^{-2}}\\\\4=b^{-2}\\\\b^2=\frac{1}{4}\\\\b=\pm \frac{1}{2}\)
Since, in exponential function \(y=ab^x\), we have b > 0.
Thus, \(b=\frac{1}{2}\)
Substituting the value in (1) gives us,
\(72=a(\frac{1}{2})^{-4}\\\\72=a\times 2^4\\\\72=16a\\\\a=\frac{9}{2}\)
Thus, the exponential function is \(y=\frac{9}{2}(\frac{1}{2})^x\).
