# How do you find the exponential function formula for the points h(0) = 3 and h(1) = 15?

Apr 19, 2018

$h \left(x\right) = 3 \cdot {5}^{x} , x \in \mathbb{R}$.

#### Explanation:

Suppose that, h(x)=a*b^x; a in RR, b in RR-{0}.

$h \left(0\right) = 3 \Rightarrow a \cdot {b}^{0} = 3 \Rightarrow a = 3$.

$h \left(1\right) = 15 \Rightarrow a \cdot {b}^{1} = 15 \Rightarrow 3 \cdot b = 15 \Rightarrow b = 5$.

$\therefore h \left(x\right) = a \cdot {b}^{x} = 3 \cdot {5}^{x} , x \in \mathbb{R}$.