A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest tenth. Show your work.

please help

Answers

Answer 1

Answer:

The half-life of this radioactive substance is of 8.6 months.

Step-by-step explanation:

Exponential decay of an amount:

The equation that models an amount after t units of time, subject to exponential decay, is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A radioactive substance decays to 30% of its original mass in 15 months.

This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]

[tex](1-r)^{15} = 0.3[/tex]

[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]

[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]

[tex]1 - r = 0.9229[/tex]

So

[tex]A(t) = A(0)(0.9229)^t[/tex]

Determine the half-life of this radioactive substance to the nearest tenth.

This is t for which A(t) = 0.5A(0). So

[tex]A(t) = A(0)(0.9229)^t[/tex]

[tex]0.5A(0) = A(0)(0.9229)^t[/tex]

[tex](0.9229)^t = 0.5[/tex]

[tex]\log{(0.9229)^t} = \log{0.5}[/tex]

[tex]t\log{0.9229} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]

[tex]t = 8.6[/tex]

The half-life of this radioactive substance is of 8.6 months.


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The area of this parallelogram is:

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Answers

Answer:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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a.

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I calculated it logically

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Answer:

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Given -

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Answer:

The options are not given so these are the options:

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Step-by-step explanation:

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I got it right on my test.

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Answers

Answer:

Dimensions : L = 12 inches, Width = 2 inches

Step-by-step explanation:

Let width be w

Let length be w + 10

Area = length x width

24 = w x (w + 10)

[tex]24 = w^2 + 10w\\\\w^2 + 10w - 24 = 0\\\\w^2 +12w -2w -24 = 0\\\\w(w+12) -2(w+12) = 0\\(w-2)(w+12)=0 \\w = 2 , -12[/tex]

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Answers

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Answers

Answer: It's B, C, F Hope it helps!

Step-by-step explanation: -3(t-7+5t+8) collect like terms -3(6t+1)

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It C to because 1. expand by distributing terms -(18t+9)+6

2. Remove parentheses -18t-9+6

3. Collect like terms -18t+(-9+6) simplify and it would give you -18t+3  it also F because I collect like terms (-3t-15t)+(21-24) and you simplify and that would give you -18t-3 as well can you make me brainliest bye!

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