Using the given points, I was able to graph the functions t(x) and p(x) as shown in the picture. The difference between a quadratic function and an exponential is the degree of the equation. The quadratic equation has a degree of 2 while that of an exponential function is a degree raised to a variable. For better illustration, I would provide examples:
Quadratic equation: y = 2x²+5
Exponential equation: y = 2³ˣ
If you would test it quantitatively the rate of change, or the slope, between points is greater for exponential than quadratic equations. Because a slight increase in x, will cause an exponential rise, To you observe visually if the slope is greater if the curve is closer to a vertical line. From the picture, we can see that the blue curve has a greater slope. Therefore, the exponential function is t(x).
Quadratic equation: y = 2x²+5
Exponential equation: y = 2³ˣ
If you would test it quantitatively the rate of change, or the slope, between points is greater for exponential than quadratic equations. Because a slight increase in x, will cause an exponential rise, To you observe visually if the slope is greater if the curve is closer to a vertical line. From the picture, we can see that the blue curve has a greater slope. Therefore, the exponential function is t(x).