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DedPeter [7]
3 years ago
6

William is going to invest $400 and leave it in an account for 8 years. Assuming the interest is compounded continuously, what i

nterest rate, to the nearest hundredth of a percent, would be required in order for William to end up with $460?
Mathematics
1 answer:
Simora [160]3 years ago
3 0

Answer:

1.75%

Step-by-step explanation:

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On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negati
Juliette [100K]

The correct option is:

As the x-values go to positive infinity, the function's values go to positive infinity.

<h3>What is the end behavior of the function?</h3>

By the description, We know that the function has the points:

(-1.25, -3.25), (0.25, -1.75) (-2.25, 0), (0, -2), (-2.75, 6), (1.5, 6)

Notice that from x = 0.25 to x = 1.5 the function goes upwards, then in the right side, the function goes up, so as x goes to positive infinity, also does f(x).

On the left side, we can see  that from x = -2.75 to x = -2.25 the function goes downwards.

So, as x goes to the left (negative infinity) f(x) goes upwards.

Then as x tends to negative infinity, f(x) tends to infinity.

The correct option is:

As the x-values go to positive infinity, the function's values go to positive infinity.

If you want to learn more about end behavior:

brainly.com/question/1365136

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8 0
2 years ago
<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%
andrey2020 [161]

First observe that if a+b>0,

(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}

Let a=0 and b=x. It follows that

a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}

Now let b=1, so a^2+a=4x. Solving for a,

a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2

which means

a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}

Now solve for x.

x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2

(note that we assume 2x-1\ge0)

4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}

(we omit x=0 since 2\cdot0-1=-1\ge0 is not true)

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What does this sign mean?
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If stock prices are falling that’s a good time to buy

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4 years ago
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I have done what you want

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3 years ago
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SelectTWO expressions that are equivalent to 8(x + 5y).
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Answer:

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