Final answer:
Priya's conclusion is incorrect because the exponential function g(x) = 3(2)^x grows at a much faster rate than the quadratic function f(x) = 10x^2 as x becomes very large, despite initial values of f(x) being higher.
Step-by-step explanation:
Priya's conclusion about the growth rates of the functions f(x) = 10x^2 and g(x) = 3(2)^x being incorrect is due to the nature of these mathematical functions. While f(x) is a quadratic function growing at a polynomial rate, g(x) is an exponential function, which generally grows much faster than a polynomial function as x becomes very large. Initially, the values of f(x) may seem higher than those of g(x), as is the case with f(1) and f(2) compared to g(1) and g(2). However, exponential growth will eventually surpass polynomial growth, meaning that there will be a point where g(x) will exceed f(x) as x continues to increase.
Graphing these functions or using limit analysis could better illustrate this point. As we approach infinity, the exponential function will grow without bounds much more rapidly than the quadratic function, thus g(x) will be greater than f(x) eventually. This can be shown mathematically by taking the limit of g(x) / f(x) as x approaches infinity, which will result in a number greater than one, signifying that g(x) grows faster than f(x) in the long run.