# How do you find the formula of an exponential graph given (0,4) and (1,4.3)?

Sep 1, 2016

$f \left(x\right) = 4 \left({1.075}^{x}\right)$

#### Explanation:

We want to fit these data points to a function of the form:

$f \left(x\right) = a \cdot {b}^{x}$

for some constants $a , b$ to be determined, with $b > 0$.

We are told:

$\left\{\begin{matrix}f \left(0\right) = 4 \\ f \left(1\right) = 4.3\end{matrix}\right.$

For any non-zero value of $b$, we have ${b}^{0} = 1$.

So we find:

$a = a \cdot {b}^{0} = f \left(0\right) = 4$

$b = \frac{a \cdot {b}^{1}}{a} = f \frac{1}{a} = \frac{4.3}{4} = 1.075$

So:

$f \left(x\right) = 4 \left({1.075}^{x}\right)$