Question

the amount 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 = ?(1 - )^

remaining amount = i(1 - r)^t

enter the number that belongs in the green box

Explanation:

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<reasoning>

Identify the given values and formula

Using the Exponential Growth Modeling knowledge point
\[

$$\begin{aligned} &\text{Formula: } \text{Remaining Amount} = I(1 - r)^t \\ &I = 50 \\ &r = 50\% = 0.5 \\ &\text{Interval: } 3 \text{ months} \\ &t = \frac{12}{3} = 4 \end{aligned}$$

\]

Match the green box value

Using the Exponential Growth Modeling knowledge point
\[

$$\begin{aligned} &\text{Remaining Amount} = 50(1 - 0.5)^4 \\ &\text{Template: } [?](1 - \Box)^{\Box} \\ &[?] = 50 \end{aligned}$$

\]
</reasoning>

<answer>
Enter the number that belongs in the green box: <blank>50</blank>
</answer>

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Answer:

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<reasoning>

Identify the given values and formula

Using the Exponential Growth Modeling knowledge point
\[

$$\begin{aligned} &\text{Formula: } \text{Remaining Amount} = I(1 - r)^t \\ &I = 50 \\ &r = 50\% = 0.5 \\ &\text{Interval: } 3 \text{ months} \\ &t = \frac{12}{3} = 4 \end{aligned}$$

\]

Match the green box value

Using the Exponential Growth Modeling knowledge point
\[

$$\begin{aligned} &\text{Remaining Amount} = 50(1 - 0.5)^4 \\ &\text{Template: } [?](1 - \Box)^{\Box} \\ &[?] = 50 \end{aligned}$$

\]
</reasoning>

<answer>
Enter the number that belongs in the green box: <blank>50</blank>
</answer>

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