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4 years ago

Write −1/2x+y=10 in slope-intercept form.

Mathematics

1 answer:

Varvara68 [4.7K]4 years ago

6 0

Answer:

$y=\frac{1}{2} x+10$

Step-by-step explanation:

$-\frac{1}{2} x+y=10\\$

<em>Add </em> $\frac{1}{2} x$ <em> to both sides</em>

$y=10+\frac{1}{2} x\\\\y=\frac{1}{2} x+10$

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4 years ago

The half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93% of

GaryK [48]

Answer:

It will take 4.84 hours for the drug to decay to 93% of the original dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is: $A = A_0 e^{kt}$

Now, we know that A becomes half after 47 hours which means that;

$A = 0.5 A_0$

Using this in the above equation we get;

$A = A_0 e^{kt}$

$0.5 A_0 = A_0 e^{(k\times 47)}$ where t = 47 hours

$\frac{0.5 A_0}{A_0} = e^{(47k)}$

$0.5 = e^{47k}$

Taking log on both sides we get;

$ln(0.5) = ln(e^{47k})$

$ln(0.5) =47k$

$k = \frac{ln(0.5)}{47}$

k = -0.015

Now, the time it will take for the drug to decay to 93% of the original dosage is given by;

$0.93 = e^{kt}$ where t is the required time

$0.93 = e^{(-0.015 \times t)}$

Taking log on both sides we get;

$ln(0.93) = ln(e^{-0.015t})$

$ln(0.93) =-0.015t$

$t = \frac{ln(0.93)}{-0.015}$

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93% of the original dosage.

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4 years ago