Question

fill in the blank 2.5 points
use the following graph to answer the questions.
when writing the equation of the exponential function graphed above, what is the a value? type your answer...
when writing the equation of the exponential function graphed above, what is the b value? type your answer...
what is the equation of the exponential function graphed above? type your answer... when typing in the equation, type in the following format.
y=(a)(b)^x

Explanation:

Step1: Recall exponential function form

The general form is \( y = a(b)^x \). At \( x = 0 \), \( y = a(b)^0 = a \). So we find the y - intercept (when \( x = 0 \)) from the graph.
Looking at the graph, when \( x = 0 \), \( y = 1 \). So \( a = 1 \).

Step2: Find a point to determine \( b \)

Let's take another point. From the graph, when \( x = 1 \), \( y = 2 \) (since the graph passes through (1, 2) approximately? Wait, wait, looking at the grid: when \( x = 0 \), \( y = 1 \); when \( x = 1 \), let's check the graph. Wait, the graph at \( x = 0 \) is (0,1), and at \( x = 1 \), let's see the y - value. Wait, maybe another point. Wait, when \( x = 0 \), \( y = 1 \) (so \( a = 1 \)). Now, let's take \( x = 1 \), what's \( y \)? Wait, the graph: let's see, the curve starts at (0,1) and goes up. Wait, maybe when \( x = 1 \), \( y = 2 \)? Wait, no, wait the grid. Wait, the y - axis: at \( x = 0 \), the point is (0,1). Then, when \( x = 1 \), let's check the graph. Wait, maybe the point (1, 2)? Wait, no, maybe (1, 2) is not correct. Wait, wait, the exponential function: let's re - examine. Wait, when \( x = 0 \), \( y = a = 1 \). Now, let's take \( x = 1 \), what's \( y \)? Wait, the graph: at \( x = 1 \), the y - coordinate seems to be 2? Wait, no, maybe (1, 2) is wrong. Wait, wait, the graph: when \( x = 0 \), \( y = 1 \); when \( x = 1 \), let's look at the grid. The vertical lines are x - axis, horizontal are y - axis. At \( x = 0 \), y = 1 (so a = 1). Now, let's take \( x = 1 \), the graph is at y = 2? Wait, no, maybe (1, 2) is correct. So plug \( x = 1 \), \( y = 2 \), \( a = 1 \) into \( y=a(b)^x \): \( 2=1\times(b)^1\), so \( b = 2 \). Wait, but let's check another point. Wait, maybe I made a mistake. Wait, the graph: when \( x = 0 \), y = 1 (so a = 1). Then, let's see, when \( x = 1 \), the graph is at y = 2? So \( b = 2 \).

Step3: Write the equation

Now that \( a = 1 \) and \( b = 2 \), the equation is \( y = 1\times(2)^x=2^x \).

Answer:

• The value of \( a \) is \( 1 \).
• The value of \( b \) is \( 2 \).
• The equation of the exponential function is \( y = 1\times(2)^x \) or \( y = 2^x \).