Question

The graphs of y = 3x and y = 3* are shown below.

Answer 1

The growth of y = 3x compare to the growth of y = 3 as the function y = 3^x is growing faster than y = 3x.

How to explain the graph?

The growth rate of any function is calculated by finding its limit at infinity. Here, 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.

Therefore, in comparison with the above sequence : The function y = 3^x is growing faster than y = 3x.

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