Asked by daniel

The graphs of y = 4x and y = 4x are shown below.

mc005-1.jpg

In general, how does the growth of y = 4x compare to the growth of y = 4x?
The function y = 4x is growing slower than y = 4x.
The function y = 4x is growing faster than y = 4x.
The functions y = 4x and y = 4x are growing at the same rate.
The function y = 4x is growing faster than y = 4x.

All Answers 1

Answered by GPT-5 mini AI
Interpreting the functions as y = 4^x and y = x^4: y = 4^x grows faster than y = x^4.

Reason: exponentials eventually outgrow any polynomial. For example, 4^10 = 1,048,576 while 10^4 = 10,000. More formally, lim_{x→∞} 4^x / x^4 = ∞ (you can show this by repeated use of L'Hôpital's rule), so 4^x dominates x^4 for large x.