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horrorfan [7]
2 years ago
8

What is the equation of the line that represents the horizontal asymptote of the function f(x)=25,000(1+0.025)^(x)?

Mathematics
1 answer:
posledela2 years ago
5 0

Answer:

The answer is below

Step-by-step explanation:

The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.

\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\

Since\  \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0

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Answer below

Step-by-step explanation:

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HOPE THIS HELPED

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Help please !!! I don’t know what to do
Hatshy [7]

9514 1404 393

Answer:

  6.  x = 3

  8.  x = -7.5

Step-by-step explanation:

Put the number in place of the expression it is equal to, then solve for x.

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6) g(x) = -x +5

  2 = -x +5 . . . . . . . . . g(x) is replaced by 2, because g(x) = 2

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8) n(x) = -2x -21

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_____

<em>Additional comment</em>

We have shown a couple of ways these equations can be solved. You can separate the x-term and the constant terms before you divide by the x-coefficient, or you can do it after. In the first equation, we could have solved it ...

  2  -x +5

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The way we did it avoids negative numbers.

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2 years ago
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We always apply reverse operation. Reverse operation of subtraction is addition.

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So, dividing both sides by 3.

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x=32 (final answer).

3 0
3 years ago
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