# How do you find the formula of an exponential graph given (0, -2) and (2, -50)?

Nov 8, 2015

Use this model: $y = a {b}^{x}$, now solve for a and b:

#### Explanation:

$y = a {b}^{x}$

Insert the x and y values into the model:

$- 2 = a {b}^{0} = a$

So, now we know that the coefficient $a = - 2$

$- 50 = \left(- 2\right) \left({b}^{2}\right)$

Solving for coefficient b ...

$b = 5$

Finally, insert both coefficients back into the model:

$y = \left(- 2\right) \left({5}^{x}\right)$

hope that helped