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goldenfox [79]
3 years ago
12

What does the equal sign with an arrow mean?

Mathematics
1 answer:
stealth61 [152]3 years ago
5 0
The <span>⇒</span><span> sign means that if the function on the left hand side of the notation is true, then so is the function on the right hand side of the notation.</span>
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HELP ME PLEASE
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Answer:

The initial mass of the sample was 16 mg.

The mass after 5 weeks will be about 0.0372 mg.

Step-by-step explanation:

We can write an exponential function to model the situation.

Let the initial amount be A. The standard exponential function is given by:

P(t)=A(r)^t

Where r is the rate of growth/decay.

Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:

\displaystyle P(t)=A\Big(\frac{1}{2}\Big)^{t/4}

After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.

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\displaystyle 2=A\Big(\frac{1}{2}\Big)^{12/4}

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\displaystyle 2=A\Big(\frac{1}{2}\Big)^3

Simplify:

\displaystyle 2=A\Big(\frac{1}{8}\Big)

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A=16\text{ mg}

5 weeks is equivalent to 35 days. Therefore, we can find P(35):

\displaystyle P(35)=16\Big(\frac{1}{2}\Big)^{35/4}\approx0.0372\text{ mg}

About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.

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