Question

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

mc004-1.jpg

In general, how does the growth of y = 3x compare to the growth of y = 3x?
The function y = 3x is growing slower than y = 3x.
The function y = 3x is growing faster than y = 3x.
The functions y = 3x and y = 3x are growing at the same rate.
The function y = 3x is growing slower than y = 3x.

Answer 1

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

Reason: for large x exponential growth dominates polynomial growth (e.g. x = 10: 3^10 = 59,049 while 10^3 = 1,000). Formally, lim_{x→∞} 3^x / x^3 = ∞, so 3^x grows much faster.