# How do I find the exponential function of the form f(x)=ab^x for which f(-1)=10 and f(0)=5?

Jan 30, 2015

The answer is: $y = 5 {\left(\frac{1}{2}\right)}^{x}$

$f \left(- 1\right) = 10 \Rightarrow 10 = a {b}^{-} 1 \Rightarrow 10 = \frac{a}{b} \Rightarrow a = 10 b$

$f \left(0\right) = 5 \Rightarrow 5 = a {b}^{0} \Rightarrow 5 = a \cdot 1 \Rightarrow a = 5$.

So:
$a = 5 \mathmr{and} b = \frac{1}{2}$.

The function is: $y = 5 {\left(\frac{1}{2}\right)}^{x}$.