### Home > INT3 > Chapter 2 > Lesson 2.2.2 > Problem2-66

2-66.

Write a possible exponential function in $y=a·b^x$ form for each graph described below.

1. Has a $y$‑intercept of $(0,3)$ and passes through the point $(2,48)$.

Substitute the coordinates of each of the given points into the general equation $y=ab^x$.
This creates a system of equations that can be solved for $a$ and $b$.

Substitute the values $0$ for $x$ and $3$ for $y$, then solve for $a$.

2. Passes through the points $(0,2)$ and $(3,0.25)$.

Create two equations substituting the coordinates of the points into the equation $y=ab^x$.

Solve the system of equations for $a$ and $b$.

Be sure you use your results for $a$ and $b$ to write the equation.

$y = 2 \cdot \left(\frac{1}{2}\right)^{x}$