Question

a pond is stocked with 150 fish, and their population increases by 20% every month. how many fish will there be after 2 months?

future amount = ? (1 + )

future amount = i(1 + r)^t

enter the number that belongs in the green box.

Explanation:

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<reasoning>

Identify the exponential growth formula components

Using the Percentage Calculations knowledge point
\[
\text{Future Amount} = I(1 + r)^t
\]
where:

• \(I\) represents the initial amount (starting population).
• \(r\) represents the growth rate as a decimal.
• \(t\) represents the time elapsed in months.

Determine the value for the initial amount

Using the Percentage Calculations knowledge point
\[

$$\begin{aligned} &I = 150\\ &r = 20\% = 0.2\\ &t = 2 \end{aligned}$$

\]

Match with the given template

Using the Percentage Calculations knowledge point
\[

$$\begin{aligned} &\text{Future Amount} = [?](1 + \text{___})^t\\ &\text{Future Amount} = 150(1 + 0.2)^2 \end{aligned}$$

\]
The green box \([?]\) corresponds to the initial amount \(I\), which is \(150\).
</reasoning>

<answer>
Enter the number that belongs in the green box.

Future Amount = <blank>150</blank>\((1 + 0.2)^2\)
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Algebra",
"Exponential Growth Modeling"
]
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Answer:

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</pre_analysis>

<reasoning>

Identify the exponential growth formula components

Using the Percentage Calculations knowledge point
\[
\text{Future Amount} = I(1 + r)^t
\]
where:

• \(I\) represents the initial amount (starting population).
• \(r\) represents the growth rate as a decimal.
• \(t\) represents the time elapsed in months.

Determine the value for the initial amount

Using the Percentage Calculations knowledge point
\[

$$\begin{aligned} &I = 150\\ &r = 20\% = 0.2\\ &t = 2 \end{aligned}$$

\]

Match with the given template

Using the Percentage Calculations knowledge point
\[

$$\begin{aligned} &\text{Future Amount} = [?](1 + \text{___})^t\\ &\text{Future Amount} = 150(1 + 0.2)^2 \end{aligned}$$

\]
The green box \([?]\) corresponds to the initial amount \(I\), which is \(150\).
</reasoning>

<answer>
Enter the number that belongs in the green box.

Future Amount = <blank>150</blank>\((1 + 0.2)^2\)
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponential Growth Modeling"
]
}
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