Question

1. theodore purchased a vintage painting from an art dealer worth $480. the dealer noted that the value of the painting will increase by 12 percent per year. what is the growth factor of the painting?

0.12
480
1.12
12

Explanation:

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<reasoning>

Identify the given values

We are given:

• Initial value of the painting: \(P = \$480\)
• Annual growth rate: \(r = 12\%\)

Define the growth factor

For exponential growth, the growth factor \(b\) is calculated using the formula:
\[b = 1 + r\]
where \(r\) is the growth rate expressed as a decimal.

Convert percentage to decimal

Convert the percentage rate to a decimal:
\[r = 12\% = 0.12\]

Calculate the growth factor

Substitute \(r = 0.12\) into the growth factor formula:
\[b = 1 + 0.12 = 1.12\]
</reasoning>

<answer>
<mcq-option>0.12</mcq-option>
<mcq-option>480</mcq-option>
<mcq-correct>1.12</mcq-correct>
<mcq-option>12</mcq-option>
</answer>

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Answer:

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</pre_analysis>

<reasoning>

Identify the given values

We are given:

• Initial value of the painting: \(P = \$480\)
• Annual growth rate: \(r = 12\%\)

Define the growth factor

For exponential growth, the growth factor \(b\) is calculated using the formula:
\[b = 1 + r\]
where \(r\) is the growth rate expressed as a decimal.

Convert percentage to decimal

Convert the percentage rate to a decimal:
\[r = 12\% = 0.12\]

Calculate the growth factor

Substitute \(r = 0.12\) into the growth factor formula:
\[b = 1 + 0.12 = 1.12\]
</reasoning>

<answer>
<mcq-option>0.12</mcq-option>
<mcq-option>480</mcq-option>
<mcq-correct>1.12</mcq-correct>
<mcq-option>12</mcq-option>
</answer>

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