The rate of growth of the functio y=3x is 3. The rate of growth of the second function is 3 too. Therefore, the rate of growth of both functions is the same.
The function y = 3^x is growing faster than y = 3x.
The growth rate of any function is calculated by finding its limit at infinity.
So, we need to calculate the limit of the function when x approaches to infinity.
Also, As x approaches infinity the order followed by the functions according to their growth rate is :
Factorial < Exponential < Polynomial < 1
Now, the function y = 3x is polynomial and the other function y = 3^x is exponential.
So, in comparison with the above sequence : The function y = 3^x is growing faster than y = 3x.