An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The end behavior of a polynomial function is determined by its leading term.
The leading term of the given polynomial is 7 x 12 .
Since the exponent is even and the coefficient is positive, as x approaches − ∞ or ∞ , y approaches ∞ .
Therefore, as x → − ∞ , y → ∞ and as x → ∞ , y → ∞ . As x → − ∞ , y → ∞ and as x → ∞ , y → ∞
Explanation
Understanding the Problem We are asked to determine the end behavior of the polynomial function y = 7 x 12 − 3 x 8 − 9 x 4 . The end behavior of a polynomial function describes what happens to the y -values as x approaches positive or negative infinity.
Identifying the Leading Term The end behavior of a polynomial is determined by its leading term, which is the term with the highest power of x . In this case, the leading term is 7 x 12 . The coefficient of the leading term is 7, which is positive, and the exponent of the leading term is 12, which is even.
Determining the End Behavior When the exponent of the leading term is even and the coefficient is positive, as x approaches either positive or negative infinity, the y -value approaches positive infinity. This is because any number raised to an even power is positive, and multiplying by a positive coefficient keeps the result positive.
Conclusion Therefore, as x r i g h t a rro w − ∞ , yr i g h t a rro w ∞ and as x r i g h t a rro w ∞ , yr i g h t a rro w ∞ .
Examples
Understanding the end behavior of polynomial functions is useful in various real-world applications. For example, when modeling population growth or decline, the end behavior can predict long-term trends. Similarly, in engineering, understanding the end behavior of functions that model physical systems can help predict stability and performance under extreme conditions. This concept is also fundamental in economics for forecasting long-term market trends based on mathematical models.
An electric device carrying a current of 15.0 A for 30 seconds will have approximately 2.81 × 1 0 21 electrons flow through it. This is calculated using the total charge formula and the charge of a single electron. Thus, the total charge of 450 C corresponds to this number of electrons.
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