# How do you write a rule for this exponential growth function if one point is at (-1,4) and the other is (0,3)?

Jul 8, 2017

Exponential growth can be written in many mathematically equivalent forms, $y = C {r}^{x} , y = C {e}^{\lambda x} , y = C {\left(1 + r\right)}^{x}$, and so on.

#### Explanation:

I will use the following:

$y = C {r}^{x}$

The point $\left(0 , 3\right)$ allows us to find the value of C:

$3 = C {r}^{0}$

Any number to the 0 power is 1:

$C = 3$

The point $\left(- 1 , 4\right)$ allows us to find the value of r:

$4 = 3 {r}^{-} 1$

$\frac{4}{3} = {r}^{-} 1$

$r = \frac{3}{4}$

$y = 3 {\left(\frac{3}{4}\right)}^{x}$

Here is a graph:

graph{3(3/4)^x [-11.25, 11.25, -5.625, 5.625]}