# How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,2); passing through P=(-1, 2/5)?

Jun 8, 2016

We know the value of $\left(x , y\right)$ in two different cases. Therefore, we need to find the value of a and b. We have enough information to write a system of equations and to solve for a and b.

#### Explanation:

$\frac{2}{5} = a \times {b}^{- 1}$

$2 = a \times {b}^{0}$

$2 = a \times 1$

$2 = a$

$\frac{2}{5} = 2 \times \frac{1}{b}$

$\frac{2}{5} = \frac{2}{b}$

$b = 5$

The equation of this function is therefore $y = 2 \times {5}^{x}$.

Hopefully this helps!