# With 300 being the y intercepts and an additional point being (3,450) How do you find a formula in the format of ab^x?

Feb 17, 2017

$y = 300 {\left(\sqrt[3]{\frac{3}{2}}\right)}^{x}$

#### Explanation:

Use the y-intercept to find $a$:

$300 = a {b}^{0}$, where ${b}^{0} = 1$ so $a = 300$ which means $y = 300 {b}^{x}$

Use the point to find $b$:

$450 = 300 {b}^{3}$; so ${b}^{3} = \frac{450}{300} = \frac{3}{2} = 1.5$

this means $b = \sqrt[3]{\frac{3}{2}} \approx 1.1447$

so $y = 300 {\left(\sqrt[3]{\frac{3}{2}}\right)}^{x} = 300 {\left(\sqrt[3]{1.5}\right)}^{x}$