# How do you write an exponential function whose graph passes through (0,7) and (2,63)?

Apr 24, 2017

$y = 7 \times {3}^{x}$ or $y = 7 \times {\left(- 3\right)}^{x}$

#### Explanation:

An exponential function is of the type $y = a {b}^{x}$

As it passes through $\left(0 , 7\right)$, we have

$7 = a \times {b}^{0}$ or $7 = a \times 1$ i.e. $a = 7$ and function is #y=7b^x

it also passes through $\left(2 , 63\right)$ and hence

$63 = 7 \times {b}^{2}$ or $7 {b}^{2} = 63$ or ${b}^{2} = 9$

and hence $b = + 3$ or $b = - 3$

and equations are $y = 7 \times {3}^{x}$ or $y = 7 \times {\left(- 3\right)}^{x}$