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 initial value of the painting?

12
0.12
480
1.12

Explanation:

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<reasoning>

Identify the given values

Using the Exponential Growth knowledge point
\[

$$\begin{aligned} &\text{Purchase value} = \$480\\ &\text{Annual growth rate } (r) = 12\% = 0.12 \end{aligned}$$

\]

Determine the initial value

Using the Exponential Growth and Growth Factor knowledge points
\[

$$\begin{aligned} &V(t) = a(1 + r)^t\\ &a = V(0) = 480 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 12</mcq-option>
<mcq-option>(B) 0.12</mcq-option>
<mcq-correct>(C) 480</mcq-correct>
<mcq-option>(D) 1.12</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given values

Using the Exponential Growth knowledge point
\[

$$\begin{aligned} &\text{Purchase value} = \$480\\ &\text{Annual growth rate } (r) = 12\% = 0.12 \end{aligned}$$

\]

Determine the initial value

Using the Exponential Growth and Growth Factor knowledge points
\[

$$\begin{aligned} &V(t) = a(1 + r)^t\\ &a = V(0) = 480 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 12</mcq-option>
<mcq-option>(B) 0.12</mcq-option>
<mcq-correct>(C) 480</mcq-correct>
<mcq-option>(D) 1.12</mcq-option>
</answer>

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