Final answer:
An exponential graph depicts a rapidly increasing growth rate over time, based on a base raised to the power of the time interval, while a quadratic graph depicts a parabolic shape with value increasing with the square of time, showing fundamentally different growth behaviors.
Step-by-step explanation:
One way in which an exponential graph is different from a quadratic graph is the nature of their growth rates over time. An exponential graph depicts exponential growth, which means that as time progresses, the rate of growth becomes increasingly rapid, following a base number raised to the power of the time interval. In other words, the graphed value increases by a factor of the base raised to the number of elapsed intervals. For example, with a base of 2 over 5 time intervals, we get 2^5=32. Conversely, a quadratic graph shows a parabolic shape, indicating that the value increases quadratically over time, which is to say, the value is proportional to the square of the elapsed time.
An exponential graph, when plotted on a logarithmic scale, can be represented by a straight line, which signifies a consistent exponential growth rate. However, a quadratic function would not appear as a straight line on a logarithmic scale.
Moreover, exponential growth can continue indefinitely under ideal conditions, as presented on the graph by an ever-increasing curve that rapidly moves away from the x-axis. Quadratic growth will appear as a symmetrical curve that opens upwards, with a rate of increase that is not as steep as exponential growth under most circumstances.