# How do you write an exponential function whose graph passes through the points (0,3) and (-1,6)?

Nov 17, 2016

#### Explanation:

Given: $\left(0 , 3\right) \mathmr{and} \left(- 1 , 6\right)$

Using the equation:

$y = a {e}^{\alpha \left(x\right)}$

Substitute 0 for x and 3 or y:

$3 = a {e}^{\alpha \left(0\right)}$

$a = 3$

Substitute 3 for a:

$y = 3 {e}^{\alpha \left(x\right)}$

Substitute -1 for x and 6 for y:

$6 = 3 {e}^{\alpha \left(- 1\right)}$

Divide by 3

$2 = {e}^{\alpha \left(- 1\right)}$

Natural log of both sides:

$\ln \left(2\right) = - \alpha$

$\alpha = \ln \left(\frac{1}{2}\right)$

Substitute $\ln \left(\frac{1}{2}\right)$ for $\alpha$:

$y = 3 {e}^{\ln \left(\frac{1}{2}\right) \left(x\right)}$

Here is the graph: