Question

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

In general, how does the growth of y = 3x compare to the growth of y = 3^x?


a. The function y = 3x is growing slower than y = 3x.
b. The function y = 3x is growing faster than y = 3x.
c. The functions y = 3x and y = 3x are growing at the same rate.
d. The function y = 3x is growing slower than y = 3x.

Answer 1

options are not clear  but y=3^x grows faster than y=3x

Answer 2

The function y = 3^x is growing faster than y = 3x.

Explanation:

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.