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3 years ago

Please help me answer this question!

Mathematics

1 answer:

AysviL [449]3 years ago

3 0

Answer:

D. -3 and 3

Step-by-step explanation:

We are given an output of 2. This means this is the value we need an input for. We need to find a number(s) that lie on the x axis and when we move up, you get an output of 2.

Option A:

If we are given an input of -2, we start at (-2, 0) and move up until we reach a point on the line. We end up lying on the point (-2, 3). Thus, the output for having an input of -2 is 3 which proves that this answer is incorrect.

Option B:

As stated above -2 has an output of 3 which is wrong. Since we know this, we can eliminate this as an option.

Option C:

If we are given an input of -3, we start at (-3, 0) and move up until we reach a point on the line. We end up lying on the point (-3, 2). Thus, the output for having an input of -2 is 2 which proves that this answer is correct.

Option D:

We know that -3 is a possible input so we just need to check 3 as an input.

If we are given an input of 3, we start at (3, 0) and move up until we reach a point on the line. We end up lying on the point (3, 2). Thus, the output for having an input of 3 is 2 which proves that this answer is also correct.

Since we know that -3 and 3 are possible inputs for an output of 2 on the graph, we need to include them both in our answer. Thus, the answer is D.

Best of Luck!

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Answer:

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Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

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To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

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$\frac{dA}{dt} = kA$

Multiply both sides by dt/A

$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

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Integrate both sides

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$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

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So, we have:

$A = Ce^{kt}$

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$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

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$500000= 1000000e^{k*6}$

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$ln(0.5) = k*6$

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$k = \frac{ln(0.5)}{6}$

$k = \frac{-0.693}{6}$

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$\frac{dA}{dt} = kA$

Where

$\frac{dA}{dt}$ = Rate

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The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

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