Question

the mass of a particular radioactive substance decreases by 50% every 3 months. if you started with 50 grams of this substance, how much of it would remain after 12 months?

remaining amount = \\(50(1 - 0.50)^4\\)

remaining amount = ? grams

round your answer to the nearest whole number.

Explanation:

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<reasoning>

Identify the given values and formula

Using the Exponential Decay Modeling knowledge point
\[

$$\begin{aligned} &A_0 = 50\\ &r = 0.50\\ &n = \frac{12}{3} = 4\\ &A = 50(1 - 0.50)^4 \end{aligned}$$

\]

Calculate the remaining amount

Using the Exponential Decay Modeling knowledge point
\[

$$\begin{aligned} &A = 50(0.50)^4\\ &A = 50(0.0625)\\ &A = 3.125 \end{aligned}$$

\]

Round to the nearest whole number

Using the Exponential Decay Modeling knowledge point
\[

$$\begin{aligned} &A \approx 3 \end{aligned}$$

\]
</reasoning>

<answer>
Remaining Amount = <blank>3</blank> grams
</answer>

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Answer:

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<reasoning>

Identify the given values and formula

Using the Exponential Decay Modeling knowledge point
\[

$$\begin{aligned} &A_0 = 50\\ &r = 0.50\\ &n = \frac{12}{3} = 4\\ &A = 50(1 - 0.50)^4 \end{aligned}$$

\]

Calculate the remaining amount

Using the Exponential Decay Modeling knowledge point
\[

$$\begin{aligned} &A = 50(0.50)^4\\ &A = 50(0.0625)\\ &A = 3.125 \end{aligned}$$

\]

Round to the nearest whole number

Using the Exponential Decay Modeling knowledge point
\[

$$\begin{aligned} &A \approx 3 \end{aligned}$$

\]
</reasoning>

<answer>
Remaining Amount = <blank>3</blank> grams
</answer>

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