For the following system, use the second equation to make a substitution for x in the first equation. x + 3y = 5 x + 7 = 2y What is the resulting equation? 1) 2 y + 2 x + 3 y = 5
2)2 y + 7 + 3 y = 5
3)2 y - 7 + 3 y = 5

Step-by-step explanation:

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)^tP(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}P(t)=A(

2

1

)

t/4

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

Therefore, when x = 12, P(x) = 2. By substitution:

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

2

1

)

12/4

Solve for A. Simplify:

\displaystyle 2=A\Big(\frac{1}{2}\Big)^32=A(

2

1

)

3

Simplify:

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

8

1

)

Thus, the initial mass of the sample was:

A=16\text{ mg}A=16 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}P(35)=16(

2

1

)

35/4

≈0.0372 mg

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

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step-by-step explanation:

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