Questions: Give the equation of the exponential function whose graph is shown. y= (Simplify your answer)

Transcript text: Give the equation of the exponential function whose graph is shown. $y=$ $\square$ (Simplify your answer)

Solution

Solution Steps

Step 1: Identify the general form of the exponential function

The general form of an exponential function is $ y = ab^x $, where $ a $ is the initial value (y-intercept) and $ b $ is the base of the exponential function.

Step 2: Determine the initial value $ a $

From the graph, we can see that the function passes through the point (0, 1). This means when $ x = 0 $, $ y = 1 $. Therefore, $ a = 1 $.

Step 3: Determine the base $ b $

To find $ b $, we use another point on the graph. The graph passes through the point (2, 25). Using the equation $ y = ab^x $ and substituting $ a = 1 $, $ x = 2 $, and $ y = 25 $:

\[ 25 = 1 \cdot b^2 \] \[ b^2 = 25 \] \[ b = 5 \]