Question

a =
b =
equation:

Explanation:

Step1: Identify the type of function

The graph is an exponential function, which has the general form \( y = ab^x \).

Step2: Find the y-intercept (when \( x = 0 \))

When \( x = 0 \), \( y = ab^0 = a(1) = a \). From the graph, when \( x = 0 \), \( y = 1 \), so \( a = 1 \).

Step3: Find the base \( b \)

Let's pick another point. Let's take \( x = 1 \). From the graph, when \( x = 1 \), \( y = 2 \) (assuming the grid is 1 unit per square). Using the equation \( y = ab^x \) with \( a = 1 \), \( x = 1 \), and \( y = 2 \):
\( 2 = 1 \times b^1 \)
So \( b = 2 \).

Step4: Write the equation

Substituting \( a = 1 \) and \( b = 2 \) into the general form, the equation is \( y = 1 \times 2^x = 2^x \).

Answer:

\( a = 1 \)
\( b = 2 \)
Equation: \( y = 2^x \)