Question

which graph shows exponential growth? (graph of a parabola opening upwards with vertex at (0,0) on a coordinate plane with x-axis from -5 to 5 and y-axis from -5 to 5)

Explanation:

Step1: Recall exponential growth graph

Exponential growth functions have the form \( y = a^x \) (\( a>1 \)), which increases rapidly as \( x \) increases, and the graph is a curve that rises steeply, not a parabola (which is quadratic, like \( y = x^2 \) shown here). But since only part of the graphs are visible, assuming there's another graph (maybe below or not fully shown) with a curve that increases exponentially (e.g., \( y = 2^x \) has a curve that starts low and rises rapidly). However, the given graph is a parabola (quadratic), so the exponential growth graph would be a curve that has a positive slope increasing as \( x \) increases, not symmetric like a parabola. If we consider typical exponential growth (e.g., \( y = e^x \) or \( y = 2^x \)), the graph should show \( y \) increasing rapidly with \( x \), with the curve getting steeper. Since the first graph is a parabola (quadratic, \( y = x^2 \)-like), the exponential growth graph would be the one with a curve that's not symmetric about the y-axis (for \( a>1 \), \( x>0 \) it rises, \( x<0 \) it approaches 0) or has a different shape. But based on the visible part, maybe the lower graph (not fully shown) is exponential. Wait, the user's image might have another graph. Assuming the standard, exponential growth graph is a curve that starts near the x-axis (for \( x \) negative) and rises steeply as \( x \) increases, while the shown graph is a parabola (quadratic). So the correct graph for exponential growth would be the one with a curve that has an increasing slope, not a U - shape.

Step2: Identify the graph

Since the given graph is a parabola (quadratic, \( y = x^2 \) - type, symmetric about y - axis), the exponential growth graph (e.g., \( y = 2^x \)) will have a curve that, for \( x>0 \), rises more steeply as \( x \) increases, and for \( x<0 \), approaches 0. If there's a graph (maybe the one below the shown parabola) with such a curve, that's the exponential growth graph. But since the user's image might have a second graph (partially shown with a rising curve), the correct graph for exponential growth is the one that is not a parabola but a curve with increasing slope (exponential curve).

Answer:

(Assuming the second graph, not fully shown, is exponential. If we consider the standard, the graph with a curve that represents \( y = a^x \) (\( a>1 \)) is the one showing exponential growth. If the options are the two graphs, and the first is a parabola, the second (the one with the rising curve, maybe the lower one) is exponential growth. So the answer would be the graph that is not the parabola, e.g., "The lower graph" or the one with the curve having an increasing slope.)