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:

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:

$$b = 1 + 0.12 = 1.12$$

Answer:

• 0.12
• 480
• 1.12 (Correct answer)
• 12