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.
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.
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