# How do you find the formula of an exponential graph given A = (1, 12) and B = (2, 48)?

Oct 30, 2015

This graph has a formula: $y = 3 \cdot \left({4}^{x}\right)$

#### Explanation:

We are looking for a function $y = a \cdot {b}^{x}$ which passes through $\left(1 , 12\right)$ and $\left(2 , 24\right)$

If we substitute the points' coordinates to the function formula we get:

$\left\{\begin{matrix}a \cdot b = 12 \\ a \cdot {b}^{2} = 48\end{matrix}\right.$

If we substitute first equation to the second we get: $12 \cdot b = 48$

so $b = 4$

Now if we substitute $b = 4$ into first equation we get: $4 a = 12$

$a = 3$

Finally we can writhe the answer: The function is: $y = 3 \cdot {4}^{x}$