Students were inquired to answer a question at school and to express what is most important for them to succeed. The one which response stood out from the rest was practice. Persons who are always successful do not become successful by being born. They work hard and perseverance their lives to succeeding. This is how you can obtain your goals. Below are one of the answer and question example that you could certainly make use of to practice and boost your information and also give you insights that could just help you to maintain your study in school.

## Question:

Plutonium-240 decays according to the function \[Q(t)=Q _{o}e ^{-kt}\] where Q represents the quantity remaining after t years and k is the decay constant, 0.00011.. How long will it take 36 grams of plutonium-240 to decay to 12 grams?. A. 18,900 years. B. 1.44 years. C. 9,990 years. D. 2,100 years.

## Answer:

The **time taken** for the 36 grams of Plutonium-240 to decay to 12 grams is **9****9****9**** ****years**** (****Option**** ****C)**

### Data obtained from the question

- Original amount (Q₀) = 36 g
- Decay constant (K) = 0.00011 /year
- Amount remaining (Q) = 12 g
**Time (t) = ?**

### How to determine the time

The time taken for the Plutonium-240 to decay from **36 g to 12 g** can be obtained as illustrated below:

Q = Q₀e^(–kt)

12 = 36 × e^(–0.00011 × t)

Divide both sides by 36

e^(–0.00011 × t) = 12 / 36

Take the Ln of both sides

–0.00011 × t = Ln (12/36)

Divide both sides by–0.0001

t = [Ln (12/36)] / –0.00011

**t = 9990 years**

Learn more about **half life**:

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